The references for Sage, sorted alphabetically by citation key.




[ABBR2012]A. Abad, R. Barrio, F. Blesa, M. Rodriguez. Algorithm 924. ACM Transactions on Mathematical Software, 39 no. 1 (2012), 1-28.
[ACFLSS04]F. N. Abu-Khzam, R. L. Collins, M. R. Fellows, M. A. Langston, W. H. Suters, and C. T. Symons: Kernelization Algorithm for the Vertex Cover Problem: Theory and Experiments. SIAM ALENEX/ANALCO 2004: 62-69.
[ADKF1970]V. Arlazarov, E. Dinic, M. Kronrod, and I. Faradzev. ‘On Economical Construction of the Transitive Closure of a Directed Graph.’ Dokl. Akad. Nauk. SSSR No. 194 (in Russian), English Translation in Soviet Math Dokl. No. 11, 1970.
[ADKLPY2014]M. R. Albrecht, B. Driessen, E. B. Kavun, G. Leander, C. Paar, and T. Yalcin, Block ciphers - focus on the linear layer (feat. PRIDE); in CRYPTO, (2014), pp. 57-76.
[AH2002]R. J. Aumann and S. Hart, Elsevier, eds. Computing equilibria for two-person games. (2002)
[AHK2015]Karim Adiprasito, June Huh, and Eric Katz. Hodge theory for combinatorial geometries. Arxiv 1511.02888.
[AHMP2008]J.-P. Aumasson, L. Henzen, W. Meier, and R. C-W Phan, Sha-3 proposal blake; in Submission to NIST, (2008).
[AHU1974]A. Aho, J. Hopcroft, and J. Ullman. ‘Chapter 6: Matrix Multiplication and Related Operations.’ The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.
[AIKMMNT2001]K. Aoki, T. Ichikawa, M. Kanda, M. Matsui, S. Moriai, J. Nakajima, and T. Tokita, Camellia: A 128-bit block cipher suitable for multiple platforms - Design and analysis; in SAC, (2000), pp. 39-56.
[Aj1996]M. Ajtai. Generating hard instances of lattice problems (extended abstract). STOC, pp. 99–108, ACM, 1996.
[AJL2011]Susumu Ariki, Nicolas Jacon, and Cedric Lecouvey. The modular branching rule for affine Hecke algebras of type A. Adv. Math. 228:481-526 (2011).
[Aki1980]J. Akiyama. and G. Exoo and F. Harary. Covering and packing in graphs. III: Cyclic and acyclic invariants. Mathematical Institute of the Slovak Academy of Sciences. Mathematica Slovaca vol 30, n 4, pages 405–417, 1980
[Al1947]A. A. Albert, A Structure Theory for Jordan Algebras. Annals of Mathematics, Second Series, Vol. 48, No. 3 (Jul., 1947), pp. 546–567.
[AL1978]A. O. L. Atkin and Wen-Ch’ing Winnie Li, Twists of newforms and pseudo-eigenvalues of \(W\)-operators. Inventiones math. 48 (1978), 221-243.
[AL2015]M. Aguiar and A. Lauve, The characteristic polynomial of the Adams operators on graded connected Hopf algebras. Algebra Number Theory, v.9, 2015, n.3, 2015.
[AM1974]J. F. Adams and H. R. Margolis, “Sub-Hopf-algebras of the Steenrod algebra,” Proc. Cambridge Philos. Soc. 76 (1974), 45-52.
[Ap1997]T. Apostol, Modular functions and Dirichlet series in number theory, Springer, 1997 (2nd ed), section 3.7–3.9.
[APR2001]George E. Andrews, Peter Paule, Axel Riese, MacMahon’s partition analysis: the Omega package, European J. Combin. 22 (2001), no. 7, 887–904.
[Ar2006]D. Armstrong. Generalized noncrossing partitions and combinatorics of Coxeter groups. Mem. Amer. Math. Soc., 2006.
[AR2012]D. Armstrong and B. Rhoades. “The Shi arrangement and the Ish arrangement”. Transactions of the American Mathematical Society 364 (2012), 1509-1528. Arxiv 1009.1655
[AS-Bessel]F. W. J. Olver: 9. Bessel Functions of Integer Order, in Abramowitz and Stegun: Handbook of Mathematical Functions.
[AS-Spherical]H. A. Antosiewicz: 10. Bessel Functions of Fractional Order, in Abramowitz and Stegun: Handbook of Mathematical Functions.
[AS-Struve]M. Abramowitz: 12. Struve Functions and Related Functions, in Abramowitz and Stegun: Handbook of Mathematical Functions.
[AS1964]M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series, 55. 1964. See also
[As2008]Sami Assaf. A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphs. FPSAC 2008, 141-152, Discrete Math. Theor. Comput. Sci. Proc., AJ, Assoc. Discrete Math. Theor. Comput. Sci., (2008). Arxiv 0804.1587v1
[AS2011]R.B.J.T Allenby and A. Slomson, “How to count”, CRC Press (2011)
[ASD1971]A. O. L. Atkin and H. P. F. Swinnerton-Dyer, “Modular forms on noncongruence subgroups”, Proc. Symp. Pure Math., Combinatorics (T. S. Motzkin, ed.), vol. 19, AMS, Providence 1971
[Av2000]D. Avis, A revised implementation of the reverse search vertex enumeration algorithm. Polytopes-combinatorics and computation. Birkhauser Basel, 2000.
[Ava2017]R. Avanzi, The QARMA block cipher family; in ToSC, (2017.1), pp. 4-44.


[Ba1994]Kaushik Basu. The Traveler’s Dilemma: Paradoxes of Rationality in Game Theory. The American Economic Review (1994): 391-395.
[BAK1998]E. Biham, R. J. Anderson, and L. R. Knudsen, Serpent: A new block cipher proposal; in FSE, (1998), pp. 222-238.
[Bar1970]Barnette, “Diagrams and Schlegel diagrams”, in Combinatorial Structures and Their Applications, Proc. Calgary Internat. Conference 1969, New York, 1970, Gordon and Breach.
[Bar2006]G. Bard. ‘Accelerating Cryptanalysis with the Method of Four Russians’. Cryptography E-Print Archive (, 2006.
[BB1997]Mladen Bestvina and Noel Brady. Morse theory and finiteness properties of groups. Invent. Math. 129 (1997). No. 3, 445-470.
[BB2009]Tomas J. Boothby and Robert W. Bradshaw. Bitslicing and the Method of Four Russians Over Larger Finite Fields. Arxiv 0901.1413, 2009.
[BBISHAR2015]S. Banik, A. Bogdanov, T. Isobe, K. Shibutani, H. Hiwatari, T. Akishita, and F. Regazzoni, Midori: A block cipher for low energy; in ASIACRYPT, (2015), pp. 411-436.
[BBKMW2013]B. Bilgin, A. Bogdanov, M, Knezevic, F. Mendel, and Q. Wang, Fides: Lightweight authenticated cipher with side-channel resistance for constrained hardware; in CHES, (2013), pp. 142-158.
[BBLSW1999]Babson, Bjorner, Linusson, Shareshian, and Welker, “Complexes of not i-connected graphs,” Topology 38 (1999), 271-299
[BPPSST2017]Banik, Pandey, Peyrin, Sasaki, Sim, and Todo, GIFT : A Small Present Towards Reaching the Limit of Lightweight Encryption. Cryptographic Hardware and Embedded Systems - CHES 2017, 2017.
[BBS1982]L. Blum, M. Blum, and M. Shub. Comparison of Two Pseudo-Random Number Generators. Advances in Cryptology: Proceedings of Crypto ‘82, pp.61–78, 1982.
[BBS1986]L. Blum, M. Blum, and M. Shub. A Simple Unpredictable Pseudo-Random Number Generator. SIAM Journal on Computing, 15(2):364–383, 1986.
[BIANCO]L. Bianco, P. Dell‘Olmo, S. Giordani An Optimal Algorithm to Find the Jump Number of Partially Ordered Sets Computational Optimization and Applications, 1997, Volume 8, Issue 2, pp 197–210, doi:10.1023/A:1008625405476
[BC1977]R. E. Bixby, W. H. Cunningham, Matroids, Graphs, and 3-Connectivity. In Graph theory and related topics (Proc. Conf., Univ. Waterloo, Waterloo, ON, 1977), 91-103
[BC2003]A. Biryukov and C. D. Canniere Block Ciphers and Systems of Quadratic Equations; in Proceedings of Fast Software Encryption 2003; LNCS 2887; pp. 274-289, Springer-Verlag 2003.
[BC2012]Mohamed Barakat and Michael Cuntz. “Coxeter and crystallographic arrangements are inductively free.” Adv. in Math. 229 Issue 1 (2012). pp. 691-709. doi:10.1016/j.aim.2011.09.011, Arxiv 1011.4228.
[BCCCNSY2010]Charles Bouillaguet, Hsieh-Chung Chen, Chen-Mou Cheng, Tung Chou, Ruben Niederhagen, Adi Shamir, and Bo-Yin Yang. Fast exhaustive search for polynomial systems in GF(2). In Stefan Mangard and François-Xavier Standaert, editors, CHES, volume 6225 of Lecture Notes in Computer Science, pages 203–218. Springer, 2010. pre-print available at
[BCGKKKLNPRRTY2012]J. Borghoff, A. Canteaut, T. Güneysu, E. B. Kavun, M. Knezevic, L. R. Knudsen, G. Leander, V. Nikov, C. Paar, C. Rechberger, P. Rombouts, S. S. Thomsen, and T. Yalcin, PRINCE - A low-latency block cipher for pervasive computing applications; in ASIACRYPT, (2012), pp. 208-225.
[BdJ2008]Besser, Amnon, and Rob de Jeu. “Li^(p)-Service? An Algorithm for Computing p-Adic Polylogarithms.” Mathematics of Computation (2008): 1105-1134.
[BD2004]M. Becker and A. Desoky. A study of the DVD content scrambling system (CSS) algorithm; in Proceedings of ISSPIT, (2004), pp. 353-356.
[BDP2013]Thomas Brüstle, Grégoire Dupont, Matthieu Pérotin On Maximal Green Sequences Arxiv 1205.2050
[BDMW2010]K. A. Browning, J. F. Dillon, M. T. McQuistan, and A. J. Wolfe, An APN permutation in dimension six; in Finite Fields: Theory and Applications - FQ9, volume 518 of Contemporary Mathematics, pages 33–42. AMS, 2010.
[BeCoMe]Frits Beukers, Henri Cohen, Anton Mellit, Finite hypergeometric functions, Arxiv 1505.02900
[Bee]Robert A. Beezer, A First Course in Linear Algebra, Accessed 15 July 2010.
[Bel2011]Belarusian State University, Information technologies. Data protection. Cryptograpic algorithms for encryption and integrity control; in STB 34.101.31-2011, (2011).
[Benasque2009]Fernando Rodriguez Villegas, The L-function of the quintic,
[Ber2008]W. Bertram : Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings, Memoirs of the American Mathematical Society, vol. 192 (2008); doi:10.1090/memo/0900; Arxiv math/0502168
[Ber1991]C. Berger, “Une version effective du théorème de Hurewicz”,
[BeukersHeckman]F. Beukers and G. Heckman, Monodromy for the hypergeometric function `{}_n F_{n-1}`, Invent. Math. 95 (1989)
[BF1999]Thomas Britz, Sergey Fomin, Finite posets and Ferrers shapes, Advances in Mathematics 158, pp. 86-127 (2001), Arxiv math/9912126 (the arXiv version has fewer errors).
[BFZ2005]A. Berenstein, S. Fomin, and A. Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells, Duke Math. J. 126 (2005), no. 1, 1–52.
[BG1980]R. L. Bishop and S. L. Goldberg, Tensor analysis on Manifolds, Dover (New York) (1980)
[BG1985]M. Blum and S. Goldwasser. An Efficient Probabilistic Public-Key Encryption Scheme Which Hides All Partial Information. In Proceedings of CRYPTO 84 on Advances in Cryptology, pp. 289–299, Springer, 1985.
[BG1988]M. Berger & B. Gostiaux : Differential Geometry: Manifolds, Curves and Surfaces, Springer (New York) (1988); doi:10.1007/978-1-4612-1033-7
[BH1994]S. Billey, M. Haiman. Schubert polynomials for the classical groups. J. Amer. Math. Soc., 1994.
[BHS2008]Robert Bradshaw, David Harvey and William Stein. strassen_window_multiply_c. strassen.pyx, Sage 3.0, 2008.
[Big1999]Stephen J. Bigelow. The Burau representation is not faithful for \(n = 5\). Geom. Topol., 3:397–404, 1999.
[Big2003]Stephen J. Bigelow, The Lawrence-Krammer representation, Geometric Topology, 2001 Georgia International Topology Conference, AMS/IP Studies in Advanced Mathematics 35 (2003). Arxiv math/0204057v1
[Bir1975]J. Birman. Braids, Links, and Mapping Class Groups, Princeton University Press, 1975
[Bj1980]Anders Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), 159-183, doi:10.1090/S0002-9947-1980-0570784-2
[BJKLMPSSS2016]C. Beierle, J. Jean, S. Kölbl, G. Leander, A. Moradi, T. Peyrin, Y. Sasaki, P. Sasdrich, and S. M. Sim, The SKINNY family of block ciphers and its low-latency variant MANTIS; in CRYPTO, (2016), pp. 123-153.
[BK1992]U. Brehm and W. Kuhnel, “15-vertex triangulations of an 8-manifold”, Math. Annalen 294 (1992), no. 1, 167-193.
[BK2001]W. Bruns and R. Koch, Computing the integral closure of an affine semigroup. Uni. Iaggelonicae Acta Math. 39, (2001), 59-70
[BKK2000]Georgia Benkart, Seok-Jin Kang, Masaki Kashiwara. Crystal bases for the quantum superalgebra \(U_q(\mathfrak{gl}(m,n))\), J. Amer. Math. Soc. 13 (2000), no. 2, 295-331.
[BKLPPRSV2007]A. Bogdanov, L. Knudsen, G. Leander, C. Paar, A. Poschmann, M. Robshaw, Y. Seurin, C. Vikkelsoe. PRESENT: An Ultra-Lightweight Block Cipher; in Proceedings of CHES 2007; LNCS 7427; pp. 450-466; Springer Verlag 2007; available at
[BL2000]Anders Björner and Frank H. Lutz, “Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere”, Experiment. Math. 9 (2000), no. 2, 275-289.
[BL2008]Corentin Boissy and Erwan Lanneau, Dynamics and geometry of the Rauzy-Veech induction for quadratic differentials (Arxiv 0710.5614) to appear in Ergodic Theory and Dynamical Systems.
[BM1940]Becker, M. F., and Saunders MacLane. The minimum number of generators for inseparable algebraic extensions. Bulletin of the American Mathematical Society 46, no. 2 (1940): 182-186.
[BM2008]John Adrian Bondy and U.S.R. Murty, “Graph theory”, Volume 244 of Graduate Texts in Mathematics, 2nd edition, Springer, 2008.
[BM2003]Bazzi and Mitter, {it Some constructions of codes from group actions}, (preprint March 2003, available on Mitter’s MIT website).
[BM2012]N. Bruin and A. Molnar, Minimal models for rational functions in a dynamical setting, LMS Journal of Computation and Mathematics, Volume 15 (2012), pp 400-417.
[BN2008]Victor V. Batyrev and Benjamin Nill. Combinatorial aspects of mirror symmetry. In Integer points in polyhedra — geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemp. Math., pages 35–66. Amer. Math. Soc., Providence, RI, 2008. Arxiv math/0703456v2.
[Bob2013]J.W. Bober. Conditionally bounding analytic ranks of elliptic curves. ANTS 10, 2013.
[Bo2009]Bosch, S., Algebra, Springer 2009
[BP1982]H. Beker and F. Piper. Cipher Systems: The Protection of Communications. John Wiley and Sons, 1982.
[BP2000]V. M. Bukhshtaber and T. E. Panov, “Moment-angle complexes and combinatorics of simplicial manifolds,” Uspekhi Mat. Nauk 55 (2000), 171–172.
[BP2015]P. Butera and M. Pernici “Sums of permanental minors using Grassmann algebra”, International Journal of Graph Theory and its Applications, 1 (2015), 83–96. Arxiv 1406.5337
[BPRS2009]J. Bastian, T. Prellberg, M. Rubey, C. Stump, Counting the number of elements in the mutation classes of `tilde{A}_n`-quivers; Arxiv 0906.0487
[BPU2016]Alex Biryukov, Léo Perrin, Aleksei Udovenko, Reverse-Engineering the S-Box of Streebog, Kuznyechik and STRIBOBr1; in EuroCrypt‘16, pp. 372-402.
[Bre2008]A. Bretscher and D. G. Corneil and M. Habib and C. Paul (2008), “A simple Linear Time LexBFS Cograph Recognition Algorithm”, SIAM Journal on Discrete Mathematics, 22 (4): 1277–1296, doi:10.1137/060664690.
[Br1910]Bruckner, “Uber die Ableitung der allgemeinen Polytope und die nach Isomorphismus verschiedenen Typen der allgemeinen Achtzelle (Oktatope)”, Verhand. Konik. Akad. Wetenschap, Erste Sectie, 10 (1910)
[Br2000]Kenneth S. Brown, Semigroups, rings, and Markov chains, Arxiv math/0006145v1.
[BR2000a]P. Barreto and V. Rijmen, The ANUBIS Block Cipher; in First Open NESSIE Workshop, (2000).
[BR2000b]P. Barreto and V. Rijmen, The Khazad legacy-level Block Cipher; in First Open NESSIE Workshop, (2000).
[BR2000c]P. Barreto and V. Rijmen, The Whirlpool hashing function; in First Open NESSIE Workshop, (2000).
[Br2016]Bresenham’s Line Algorithm, Python, 26 December 2016.
[Bru1994]Richard A. Brualdi, Hyung Chan Jung, William T.Trotter Jr On the poset of all posets on `n` elements Volume 50, Issue 2, 6 May 1994, Pages 111-123 Discrete Applied Mathematics
[Bruin-Molnar]N. Bruin and A. Molnar, Minimal models for rational functions in a dynamical setting, LMS Journal of Computation and Mathematics, Volume 15 (2012), pp 400-417.
[BS1996]Eric Bach, Jeffrey Shallit. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. MIT Press, 1996. ISBN 978-0262024051.
[BS2003]I. Bouyukliev and J. Simonis, Some new results on optimal codes over \(F_5\), Designs, Codes and Cryptography 30, no. 1 (2003): 97-111,
[BS2011]E. Byrne and A. Sneyd, On the Parameters of Codes with Two Homogeneous Weights. WCC 2011-Workshop on coding and cryptography, pp. 81-90. 2011.
[BS2012]Jonathan Bloom and Dan Saracino, Modified growth diagrams, permutation pivots, and the BWX map `Phi^*`, Journal of Combinatorial Theory, Series A Volume 119, Number 6 (2012), pp. 1280-1298.
[BSS2009]David Bremner, Mathieu Dutour Sikiric, Achill Schuermann: Polyhedral representation conversion up to symmetries, Proceedings of the 2006 CRM workshop on polyhedral computation, AMS/CRM Lecture Notes, 48 (2009), 45-71. Arxiv math/0702239
[BSV2010]M. Bolt, S. Snoeyink, E. Van Andel. “Visual representation of the Riemann map and Ahlfors map via the Kerzman-Stein equation”. Involve 3-4 (2010), 405-420.
[BW1996]Anders Bjorner and Michelle L. Wachs. Shellable nonpure complexes and posets. I. Trans. of Amer. Math. Soc. 348 No. 4. (1996)
[BZ01]A. Berenstein, A. Zelevinsky Tensor product multiplicities, canonical bases and totally positive varieties Invent. Math. 143 No. 1. (2002), 77-128.


[Car1972]R. W. Carter. Simple groups of Lie type, volume 28 of Pure and Applied Mathematics. John Wiley and Sons, 1972.
[CS1996]G. Call and J. Silverman. Computing the Canonical Height on K3 Surfaces. Mathematics of Comp. , 65 (1996), 259-290.
[CB2007]Nicolas Courtois, Gregory V. Bard: Algebraic Cryptanalysis of the Data Encryption Standard, In 11-th IMA Conference, Cirencester, UK, 18-20 December 2007, Springer LNCS 4887. See also
[CC1982]Chottin and R. Cori, Une preuve combinatoire de la rationalité d’une série génératrice associée aux arbres, RAIRO, Inf. Théor. 16, 113–128 (1982)
[CDL2015]A. Canteaut, Sebastien Duval, Gaetan Leurent Construction of Lightweight S-Boxes using Feistel and MISTY Structures; in Proceedings of SAC 2015; LNCS 9566; pp. 373-393; Springer-Verlag 2015; available at
[CE2001]Raul Cordovil and Gwihen Etienne. A note on the Orlik-Solomon algebra. Europ. J. Combinatorics. 22 (2001). pp. 165-170.
[Cer1994]D. P. Cervone, “Vertex-minimal simplicial immersions of the Klein bottle in three-space”, Geom. Ded. 50 (1994) 117-141,
[CEW2011]Georgios Chalkiadakis, Edith Elkind, and Michael Wooldridge. Computational Aspects of Cooperative Game Theory. Morgan & Claypool Publishers, (2011). ISBN 9781608456529, doi:10.2200/S00355ED1V01Y201107AIM016.
[CGW2013]Daniel Cabarcas, Florian Göpfert, and Patrick Weiden. Provably Secure LWE-Encryption with Uniform Secret. Cryptology ePrint Archive, Report 2013/164. 2013. 2013/164.
[CGMRV16]A. Conte, R. Grossi, A. Marino, R. Rizzi, L. Versari, “Directing Road Networks by Listing Strong Orientations.”, Combinatorial Algorithms, Proceedings of 27th International Workshop, IWOCA 2016, August 17-19, 2016, pages 83–95.
[Ch2012]Cho-Ho Chu. Jordan Structures in Geometry and Analysis. Cambridge University Press, New York. 2012. IBSN 978-1-107-01617-0.
[Cha92]Chameni-Nembua C. and Monjardet B. Les Treillis Pseudocomplémentés Finis Europ. J. Combinatorics (1992) 13, 89-107.
[ChLi]F. Chapoton and M. Livernet, Pre-Lie algebras and the rooted trees operad, International Math. Research Notices (2001) no 8, pages 395-408. Preprint: Arxiv math/0002069v2.
[Cha2006]Ruth Charney. An introduction to right-angled Artin groups., Arxiv math/0610668.
[ChenDB]Eric Chen, Online database of two-weight codes,
[CHK2001]Keith D. Cooper, Timothy J. Harvey and Ken Kennedy. A Simple, Fast Dominance Algorithm, Software practice and Experience, 4:1-10 (2001).
[CHPSS18]C. Cid, T. Huang, T. Peyrin, Y. Sasaki, L. Song. Boomerang Connectivity Table: A New Cryptanalysis Tool (2018) IACR Transactions on Symmetric Cryptology. Vol 2017, Issue 4. pre-print available at
[CK1999]David A. Cox and Sheldon Katz. Mirror symmetry and algebraic geometry, volume 68 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1999.
[CK2001]M. Casella and W. Kühnel, “A triangulated K3 surface with the minimum number of vertices”, Topology 40 (2001), 753–772.
[CKS1999]Felipe Cucker, Pascal Koiran, and Stephen Smale. A polynomial-time algorithm for diophantine equations in one variable, J. Symbolic Computation 27 (1), 21-29, 1999.
[CK2015]J. Campbell and V. Knight. On testing degeneracy of bi-matrix games. (2015)
[CL2013]Maria Chlouveraki and Sofia Lambropoulou. The Yokonuma-Hecke algebras and the HOMFLYPT polynomial. (2015) Arxiv 1204.1871v4.
[CLRS2001]Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein, Section 22.4: Topological sort, Introduction to Algorithms (2nd ed.), MIT Press and McGraw-Hill, 2001, 549-552, ISBN 0-262-03293-7.
[CLS2014]C. Ceballos, J.-P. Labbé, C. Stump, Subword complexes, cluster complexes, and generalized multi-associahedra, J. Algebr. Comb. 39 (2014) pp. 17-51. doi:10.1007/s10801-013-0437-x, Arxiv 1108.1776.
[CLS2011]David A. Cox, John Little, and Hal Schenck. Toric Varieties. Volume 124 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2011.
[CMO2011]C. Chun, D. Mayhew, J. Oxley, A chain theorem for internally 4-connected binary matroids. J. Combin. Theory Ser. B 101 (2011), 141-189.
[CMO2012]C. Chun, D. Mayhew, J. Oxley, Towards a splitter theorem for internally 4-connected binary matroids. J. Combin. Theory Ser. B 102 (2012), 688-700.
[CMR2005]C. Cid, S. Murphy, M. Robshaw Small Scale Variants of the AES; in Proceedings of Fast Software Encryption 2005; LNCS 3557; Springer Verlag 2005; available at
[CMR2006]C. Cid, S. Murphy, and M. Robshaw Algebraic Aspects of the Advanced Encryption Standard; Springer Verlag 2006
[CMT2003]A. M. Cohen, S. H. Murray, D. E. Talyor. Computing in groups of Lie type. Mathematics of Computation. 73 (2003), no 247. pp. 1477–1498.
[Co1984]J. Conway, Hexacode and tetracode - MINIMOG and MOG. Computational group theory, ed. M. Atkinson, Academic Press, 1984.
[Co1999]John Conway, Neil Sloan. Sphere Packings, Lattices and Groups, Springer Verlag 1999.
[Coh1993]Henri Cohen. A Course in Computational Number Theory. Graduate Texts in Mathematics 138. Springer, 1993.
[Coh2007I]Henri Cohen, Number Theory, Vol. I: Tools and Diophantine Equations. GTM 239, Springer, 2007.
[Coh2007]Henri Cohen, Number Theory, Volume II. Graduate Texts in Mathematics 240. Springer, 2007.
[Col2013]Julia Collins. An algorithm for computing the Seifert matrix of a link from a braid representation. (2013).
[Con]Keith Conrad, Groups of order 12,, accessed 21 October 2009.
[Con2013]Keith Conrad: Exterior powers,
[Con2015]Keith Conrad: Tensor products,
[CP2001]John Crisp and Luis Paris. The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group. Invent. Math. 145 (2001). No 1, 19-36. Arxiv math/0003133.
[CPdA2014]Maria Chlouveraki and Loic Poulain d’Andecy. Representation theory of the Yokonuma-Hecke algebra. (2014) Arxiv 1302.6225v2.
[CR1962]Curtis, Charles W.; Reiner, Irving “Representation theory of finite groups and associative algebras.” Pure and Applied Mathematics, Vol. XI Interscience Publishers, a division of John Wiley & Sons, New York-London 1962, pp 545–547
[Cre1997]J. E. Cremona, Algorithms for Modular Elliptic Curves. Cambridge University Press, 1997.
[Cre2003]Cressman, Ross. Evolutionary dynamics and extensive form games. MIT Press, 2003.
[Crossproduct]Algebraic Properties of the Cross Product Wikipedia article Cross_product
[CRV2018]Xavier Caruso, David Roe and Tristan Vaccon. ZpL: a p-adic precision package, (2018) Arxiv 1802.08532.
[CRV2014]Xavier Caruso, David Roe and Tristan Vaccon. Tracking p-adic precision, LMS J. Comput. Math. 17 (2014), 274-294.
[CS1986]J. Conway and N. Sloane. Lexicographic codes: error-correcting codes from game theory, IEEE Trans. Infor. Theory 32 (1986) 337-348.
[Cu1984]R. Curtis, The Steiner system \(S(5,6,12)\), the Mathieu group \(M_{12}\), and the kitten. Computational group theory, ed. M. Atkinson, Academic Press, 1984.
[Cun1986]W. H. Cunningham, Improved Bounds for Matroid Partition and Intersection Algorithms. SIAM Journal on Computing 1986 15:4, 948-957


[Dat2007]Basudeb Datta, “Minimal triangulations of manifolds”, J. Indian Inst. Sci. 87 (2007), no. 4, 429-449.
[Dav1997]B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 1997.
[DCSW2008]C. De Canniere, H. Sato, D. Watanabe, Hash Function Luffa: Specification; submitted to NIST SHA-3 Competition, 2008. Available at
[DCW2016]Dan-Cohen, Ishai, and Stefan Wewers. “Mixed Tate motives and the unit equation.” International Mathematics Research Notices 2016.17 (2016): 5291-5354.
[DD2010]Tim Dokchitser and Vladimir Dokchitser, On the Birch-Swinnerton-Dyer quotients modulo squares, Ann. Math. (2) 172 (2010), 567-596.
[DDLL2013]Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky. Lattice Signatures and Bimodal Gaussians; in Advances in Cryptology – CRYPTO 2013; Lecture Notes in Computer Science Volume 8042, 2013, pp 40-56
[Dec1998]W. Decker and T. de Jong. Groebner Bases and Invariant Theory in Groebner Bases and Applications. London Mathematical Society Lecture Note Series No. 251. (1998) 61–89.
[DEMS2016]C. Dobraunig, M. Eichlseder, F. Mendel, and M. Schläffer, Ascon v1.2; in CAESAR Competition, (2016).
[De1973]P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep., Suppl., vol. 10, 1973.
[De1974]M. Demazure, Desingularisation des varietes de Schubert, Ann. E. N. S., Vol. 6, (1974), p. 163-172
[Deh2011]P. Dehornoy, Le probleme d’isotopie des tresses, in Leçons mathématiques de Bordeaux, vol. 4, pages 259-300, Cassini (2011).
[deG2000]Willem A. de Graaf. Lie Algebras: Theory and Algorithms. North-Holland Mathematical Library. (2000). Elsevier Science B.V.
[Deo1987a]V. Deodhar, A splitting criterion for the Bruhat orderings on Coxeter groups. Comm. Algebra, 15:1889-1894, 1987.
[Deo1987b]V.V. Deodhar, On some geometric aspects of Bruhat orderings II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Alg. 111 (1987) 483-506.
[Dev2005]Devaney, Robert L. An Introduction to Chaotic Dynamical Systems. Boulder: Westview, 2005, 331.
[DGRB2010]David Avis, Gabriel D. Rosenberg, Rahul Savani, Bernhard von Stengel. Enumeration of Nash equilibria for two-player games. (2010)
[DHSW2003]Dumas, Heckenbach, Saunders, Welker, “Computing simplicial homology based on efficient Smith normal form algorithms,” in “Algebra, geometry, and software systems” (2003), 177-206.
[DI1989]Dan Gusfield and Robert W. Irving. The stable marriage problem: structure and algorithms. Vol. 54. Cambridge: MIT press, 1989.
[DI1995]F. Diamond and J. Im, Modular forms and modular curves. In: V. Kumar Murty (ed.), Seminar on Fermat’s Last Theorem (Toronto, 1993-1994), 39-133. CMS Conference Proceedings 17. American Mathematical Society, 1995.
[Dil1940]Lattice with Unique Irreducible Decompositions R. P. Dilworth, 1940 (Annals of Mathematics 41, 771-777) With comments by B. Monjardet
[Di2000]L. Dissett, Combinatorial and computational aspects of finite geometries, 2000,
[DLHK2007]J. A. De Loera, D. C. Haws, M. Köppe, Ehrhart polynomials of matroid polytopes and polymatroids. Discrete & Computational Geometry, Volume 42, Issue 4. Arxiv 0710.4346, doi:10.1007/s00454-008-9120-8
[DLMF-Bessel]F. W. J. Olver and L. C. Maximon: 10. Bessel Functions, in NIST Digital Library of Mathematical Functions.
[DLMF-Error]N. M. Temme: 7. Error Functions, Dawson’s and Fresnel Integrals, in NIST Digital Library of Mathematical Functions.
[DLMF-Struve]R. B. Paris: 11. Struve and Related Functions, in NIST Digital Library of Mathematical Functions.
[DLRS2010]De Loera, Rambau and Santos, “Triangulations: Structures for Algorithms and Applications”, Algorithms and Computation in Mathematics, Volume 25, Springer, 2011.
[DN1990]Claude Danthony and Arnaldo Nogueira “Measured foliations on nonorientable surfaces”, Annales scientifiques de l’Ecole Normale Superieure, Ser. 4, 23, no. 3 (1990) p 469-494
[Do2009]P. Dobcsanyi et al.
[DPV2001]J. Daemen, M. Peeters, and G. Van Assche, Bitslice ciphers and power analysis attacks; in FSE, (2000), pp. 134-149.
[DP2008]Jean-Guillaume Dumas and Clement Pernet. Memory efficient scheduling of Strassen-Winograd’s matrix multiplication algorithm. Arxiv 0707.2347v1, 2008.
[DPVAR2000]J. Daemen, M. Peeters, G. Van Assche, and V. Rijmen, Nessie proposal: NOEKEON; in First Open NESSIE Workshop, (2000).
[DR2002]Joan Daemen, Vincent Rijmen. The Design of Rijndael. Springer-Verlag Berlin Heidelberg, 2002.
[Dro1987]Carl Droms. Isomorphisms of graph groups. Proc. of the Amer. Math. Soc. 100 (1987). No 3.
[Du2003]I. Duursma, “Extremal weight enumerators and ultraspherical polynomials”, Discrete Mathematics 268 (2003), 103–127.
[Du2009]Du Ye. On the Complexity of Deciding Degeneracy in Games. Arxiv 0905.3012v1 (2009)
[DW1995]Andreas W.M. Dress and Walter Wenzel, A Simple Proof of an Identity Concerning Pfaffians of Skew Symmetric Matrices, Advances in Mathematics, volume 112, Issue 1, April 1995, pp. 120-134.
[DW2007]I. Dynnikov and B. Wiest, On the complexity of braids, J. Europ. Math. Soc. 9 (2007)


[Eb1989]W. Eberly, “Computations for algebras and group representations”. Ph.D. Thesis, University of Toronto, 1989.
[Ed1974]A. R. Edmonds, ‘Angular Momentum in Quantum Mechanics’, Princeton University Press (1974)
[Eh2013]Ehrhardt, Wolfgang. “The AMath and DAMath Special Functions: Reference Manual and Implementation Notes, Version 1.3”. 2013.
[EM2001]Pavel Etingof and Xiaoguang Ma. Lecture notes on Cherednik algebras. Arxiv 1001.0432.
[EP2013]David Einstein, James Propp. Combinatorial, piecewise-linear, and birational homomesy for products of two chains. Arxiv 1310.5294v1.
[EP2013b]David Einstein, James Propp. Piecewise-linear and birational toggling. Extended abstract for FPSAC 2014.
[ERH2015]Jorge Espanoza and Steen Ryom-Hansen. Cell structures for the Yokonuma-Hecke algebra and the algebra of braids and ties. (2015) Arxiv 1506.00715.
[ESSS2012]D. Engels, M.-J. O. Saarinen, P. Schweitzer, and E. M. Smith, The Hummingbird-2 lightweight authenticated encryption algorithm; in RFIDSec, (2011), pp. 19-31.
[ETS2006a]ETSI/Sage, Specification of the 3GPP Confidentiality and Integrity Algorithms UEA2 & UIA2; in Document 5: Design and Evaluation Report, (2006).
[ETS2011]ETSI/Sage, Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3; in Document 4: Design and Evaluation Report, (2011).
[Ewa1996]Ewald, “Combinatorial Convexity and Algebraic Geometry”, vol. 168 of Graduate Texts in Mathematics, Springer, 1996
[EZ1950]S. Eilenberg and J. Zilber, “Semi-Simplicial Complexes and Singular Homology”, Ann. Math. (2) 51 (1950), 499-513.
[EPW14]Ben Elias, Nicholas Proudfoot, and Max Wakefield. The Kazhdan-Lusztig polynomial of a matroid. 2014. Arxiv 1412.7408.


[Fedorov2015]Roman Fedorov, Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundles, Arxiv 1505.01704
[Fe1997]Stefan Felsner, “On the Number of Arrangements of Pseudolines”, Proceedings SoCG 96, 30-37. Discrete & Computational Geometry 18 (1997), 257-267.
[FT00]Stefan Felsner, William T. Trotter, Dimension, Graph and Hypergraph Coloring, Order, 2000, Volume 17, Issue 2, pp 167-177,
[Fe2012]Hans L. Fetter, “A Polyhedron Full of Surprises”, Mathematics Magazine 85 (2012), no. 5, 334-342.
[Fed2015]Federal Agency on Technical Regulation and Metrology (GOST), GOST R 34.12-2015, (2015)
[Feu2009]T. Feulner. The Automorphism Groups of Linear Codes and Canonical Representatives of Their Semilinear Isometry Classes. Advances in Mathematics of Communications 3 (4), pp. 363-383, Nov 2009
[Feu2013]Feulner, Thomas, “Eine kanonische Form zur Darstellung aequivalenter Codes – Computergestuetzte Berechnung und ihre Anwendung in der Codierungstheorie, Kryptographie und Geometrie”, Dissertation, University of Bayreuth, 2013.
[FH2015]J. A. de Faria, B. Hutz. Combinatorics of Cycle Lengths on Wehler K3 Surfaces over finite fields. New Zealand Journal of Mathematics 45 (2015), 19–31.
[FM2014]Cameron Franc and Marc Masdeu, “Computing fundamental domains for the Bruhat-Tits tree for GL_2(Qp), p-adic automorphic forms, and the canonical embedding of Shimura curves”. LMS Journal of Computation and Mathematics (2014), volume 17, issue 01, pp. 1-23.
[FMV2014]Xander Faber, Michelle Manes, and Bianca Viray. Computing Conjugating Sets and Automorphism Groups of Rational Functions. Journal of Algebra, 423 (2014), 1161-1190.
[Fom1994]Sergey V. Fomin, “Duality of graded graphs”. Journal of Algebraic Combinatorics Volume 3, Number 4 (1994), pp. 357-404.
[Fom1995]Sergey V. Fomin, “Schensted algorithms for dual graded graphs”. Journal of Algebraic Combinatorics Volume 4, Number 1 (1995), pp. 5-45.
[FOS2010]G. Fourier, M. Okado, A. Schilling. Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types. Contemp. Math. 506 (2010) 127-143 ( Arxiv 0811.1604 )
[FP1996]Komei Fukuda, Alain Prodon: Double Description Method Revisited, Combinatorics and Computer Science, volume 1120 of Lecture Notes in Computer Science, page 91-111. Springer (1996)
[FR1985]Friedl, Katalin, and Lajos Rónyai. “Polynomial time solutions of some problems of computational algebra”. Proceedings of the seventeenth annual ACM symposium on Theory of computing. ACM, 1985.
[FRT1990]Faddeev, Reshetikhin and Takhtajan. Quantization of Lie Groups and Lie Algebras. Leningrad Math. J. vol. 1 (1990), no. 1.
[FS2009]Philippe Flajolet and Robert Sedgewick, Analytic combinatorics. Cambridge University Press, Cambridge, 2009. See also the Errata list.
[FST2012]A. Felikson, M. Shapiro, and P. Tumarkin, Cluster Algebras of Finite Mutation Type Via Unfoldings, Int Math Res Notices (2012) 2012 (8): 1768-1804.
[Fu1993]Wiliam Fulton, Introduction to Toric Varieties, Princeton University Press, 1993.
[FY2004]Eva Maria Feichtner and Sergey Yuzvinsky. Chow rings of toric varieties defined by atomic lattices. Inventiones Mathematicae. 155 (2004), no. 3, pp. 515-536.
[FZ2007]S. Fomin and A. Zelevinsky, Cluster algebras IV. Coefficients, Compos. Math. 143 (2007), no. 1, 112-164.


[Ga02]Shuhong Gao, A new algorithm for decoding Reed-Solomon Codes, January 31, 2002
[Gambit]Richard D. McKelvey, Andrew M. McLennan, and Theodore L. Turocy, Gambit: Software Tools for Game Theory, Version 13.1.2.. (2014).
[Gar2015]V. Garg Introduction to Lattice Theory with Computer Science Applications (2015), Wiley.
[GDR1999]R. González-Díaz and P. Réal, A combinatorial method for computing Steenrod squares in J. Pure Appl. Algebra 139 (1999), 89-108.
[GDR2003]R. González-Díaz and P. Réal, Computation of cohomology operations on finite simplicial complexes in Homology, Homotopy and Applications 5 (2003), 83-93.
[Ge2005]Loukas Georgiadis, Linear-Time Algorithms for Dominators and Related Problems, PhD thesis, Princetown University, TR-737-05, (2005).
[GG2012]Jim Geelen and Bert Gerards, Characterizing graphic matroids by a system of linear equations, submitted, 2012. Preprint:
[GGD2011]E. Girondo, G. Gonzalez-Diez, Introduction to Compact Riemann surfaces and Dessins d’enfant, (2011) London Mathematical Society, Student Text 79.
[GGNS2013]B. Gerard, V. Grosso, M. Naya-Plasencia, and F.-X. Standaert, Block ciphers that are easier to mask: How far can we go?; in CHES, (2013), pp. 383-399.
[GGOR2003]V. Ginzberg, N. Guay, E. Opdam, R. Rouquier. On the category `mathcal{O}` for rational Cherednik algebras. Invent. Math. 154 (2003). Arxiv math/0212036.
[GHJV1994]E. Gamma, R. Helm, R. Johnson, J. Vlissides, Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley (1994). ISBN 0-201-63361-2.
[GK2013]Roland Grinis and Alexander Kasprzyk, Normal forms of convex lattice polytopes, Arxiv 1301.6641
[GKZ1994]Gelfand, I. M.; Kapranov, M. M.; and Zelevinsky, A. V. “Discriminants, Resultants and Multidimensional Determinants” Birkhauser 1994
[GL1996]G. Golub and C. van Loan. Matrix Computations. 3rd edition, Johns Hopkins Univ. Press, 1996.
[GLSVJGK2014]V. Grosso, G. Leurent, F.-X. Standaert, K. Varici, F. D. A. Journault, L. Gaspar, and S. Kerckhof, SCREAM & iSCREAM Side-Channel Resistant Authenticated Encryption with Masking; in CAESAR Competition, (2014).
[GM2002]Daniel Goldstein and Andrew Mayer. On the equidistribution of Hecke points. Forum Mathematicum, 15:2, pp. 165–189, De Gruyter, 2003.
[GMN2008]Jordi Guardia, Jesus Montes, Enric Nart. Newton polygons of higher order in algebraic number theory (2008). Arxiv 0807.2620
[GNL2011]Z. Gong, S. Nikova, and Y. W. Law, KLEIN: A new family of lightweight block ciphers; in RFIDSec, (2011), p. 1-18.
[Go1967]Solomon Golomb, Shift register sequences, Aegean Park Press, Laguna Hills, Ca, 1967
[God1968]R. Godement: Algebra, Hermann (Paris) / Houghton Mifflin (Boston) (1968)
[Gor1980]Daniel Gorenstein, Finite Groups (New York: Chelsea Publishing, 1980)
[Gor2009]Alexey G. Gorinov, “Combinatorics of double cosets and fundamental domains for the subgroups of the modular group”, preprint Arxiv 0901.1340
[GP2012]Eddy Godelle and Luis Paris. Basic questions on Artin-Tits groups. A. Bjorner et al. (eds) Configuration spaces, CRM series. (2012) pp. 299–311. Edizioni della Normale, Pisa. doi:10.1007/978-88-7642-431-1_13
[GPV2008]Craig Gentry, Chris Peikert, Vinod Vaikuntanathan. How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions. STOC 2008.
[GR2001]C.Godsil and G.Royle, Algebraic Graph Theory. Graduate Texts in Mathematics, Springer, 2001.
[Gr2007]J. Green, Polynomial representations of \(GL_n\), Springer Verlag, 2007.
[GriRei16]Darij Grinberg, Victor Reiner, Hopf Algebras in Combinatorics, Arxiv 1409.8356v4.
[GR2013]Darij Grinberg, Tom Roby. Iterative properties of birational rowmotion.
[GroLar1]R. Grossman and R. G. Larson, Hopf-algebraic structure of families of trees, J. Algebra 126 (1) (1989), 184-210. Preprint: Arxiv 0711.3877v1
[Grinb2016a]Darij Grinberg, Double posets and the antipode of QSym, Arxiv 1509.08355v3.
[GrS1967]Grunbaum and Sreedharan, “An enumeration of simplicial 4-polytopes with 8 vertices”, J. Comb. Th. 2, 437-465 (1967)
[GS1999]Venkatesan Guruswami and Madhu Sudan, Improved Decoding of Reed-Solomon Codes and Algebraic-Geometric Codes, 1999
[GT1996]P. Gianni and B. Trager. “Square-free algorithms in positive characteristic”. Applicable Algebra in Engineering, Communication and Computing, 7(1), 1-14 (1996)
[GT2014]M.S. Gowda and J. Tao. On the bilinearity rank of a proper cone and Lyapunov-like transformations. Mathematical Programming, 147 (2014) 155-170.
[Gu]GUAVA manual,
[GW2014]G. Gratzer and F. Wehrung, Lattice Theory: Special Topics and Applications Vol. 1, Springer, 2014.
[GZ1983]Greene; Zaslavsky, “On the Interpretation of Whitney Numbers Through Arrangements of Hyperplanes, Zonotopes, Non-Radon Partitions, and Orientations of Graphs”. Transactions of the American Mathematical Society, Vol. 280, No. 1. (Nov., 1983), pp. 97-126.


[Ha2005]Gerhard Haring. [Online] Available:
[Hac2016]M. Hachimori.
[Hai1989]M.D. Haiman, On mixed insertion, symmetry, and shifted Young tableaux. Journal of Combinatorial Theory, Series A Volume 50, Number 2 (1989), pp. 196-225.
[Hat2002]Allen Hatcher, “Algebraic Topology”, Cambridge University Press (2002).
[He2002]H. Heys A Tutorial on Linear and Differential Cryptanalysis ; 2002’ available at
[Hes2002]F. Hess, “Computing Riemann-Roch spaces in algebraic function fields and related topics,” J. Symbolic Comput. 33 (2002), no. 4, 425–445.
[Hig2008]N. J. Higham, “Functions of matrices: theory and computation”, Society for Industrial and Applied Mathematics (2008).
[HJ2004]Tom Hoeholdt and Joern Justesen, A Course In Error-Correcting Codes, EMS, 2004
[HKOTY1999]G. Hatayama, A. Kuniba, M. Okado, T. Tagaki, and Y. Yamada, Remarks on fermionic formula. Contemp. Math., 248 (1999).
[HKP2010]T. J. Haines, R. E. Kottwitz, A. Prasad, Iwahori-Hecke Algebras, J. Ramanujan Math. Soc., 25 (2010), 113–145. Arxiv 0309168v3 MathSciNet MR2642451
[HL2014]Thomas Hamilton and David Loeffler, “Congruence testing for odd modular subgroups”, LMS J. Comput. Math. 17 (2014), no. 1, 206-208, doi:10.1112/S1461157013000338.
[Hli2006]Petr Hlineny, “Equivalence-free exhaustive generation of matroid representations”, Discrete Applied Mathematics 154 (2006), pp. 1210-1222.
[HLY2002]Yi Hu, Chien-Hao Liu, and Shing-Tung Yau. Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces. Adv. Theor. Math. Phys., 6(3):457-506, 2002. Arxiv math/0010082v2 [math.AG].
[Hoc]Winfried Hochstaettler, “About the Tic-Tac-Toe Matroid”, preprint.
[HN2006]Florent Hivert and Janvier Nzeutchap. Dual Graded Graphs in Combinatorial Hopf Algebras.
[HP2003]W. C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, 2003.
[HP2016]S. Hopkins, D. Perkinson. “Bigraphical Arrangements”. Transactions of the American Mathematical Society 368 (2016), 709-725. Arxiv 1212.4398
[HPS2008]J. Hoffstein, J. Pipher, and J.H. Silverman. An Introduction to Mathematical Cryptography. Springer, 2008.
[HPS2017]Graham Hawkes, Kirill Paramonov, and Anne Schilling. Crystal analysis of type \(C\) Stanley symmetric functions. Electronic J. Comb. 24(3) (2017) #P3.51. Arxiv 1704.00889.
[HOLM2016]Tristan Holmes and J. B. Nation, Inflation of finite lattices along all-or-nothing sets.
[HR2016]Clemens Heuberger and Roswitha Rissner, “Computing \(J\)-Ideals of a Matrix Over a Principal Ideal Domain”, Arxiv 1611.10308, 2016.
[HRS1993]C. D. Hodgson, I. Rivin and W. D. Smith. A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere. Bulletin of the American Mathematical Society 27.2 (1992): 246-251.
[HRT2000]R.B. Howlett, L.J. Rylands, and D.E. Taylor. Matrix generators for exceptional groups of Lie type. J. Symbolic Computation. 11 (2000).
[Hsu1996]Tim Hsu, “Identifying congruence subgroups of the modular group”, Proc. AMS 124, no. 5, 1351-1359 (1996)
[Hsu1997]Tim Hsu, “Permutation techniques for coset representations of modular subgroups”, in L. Schneps (ed.), Geometric Galois Actions II: Dessins d’Enfants, Mapping Class Groups and Moduli, volume 243 of LMS Lect. Notes, 67-77, Cambridge Univ. Press (1997)
[Hutz2007]B. Hutz. Arithmetic Dynamics on Varieties of dimension greater than one. PhD Thesis, Brown University 2007
[Hutz2009]B. Hutz. Good reduction of periodic points, Illinois Journal of Mathematics 53 (Winter 2009), no. 4, 1109-1126.
[Hutz2015]B. Hutz. Determination of all rational preperiodic points for morphisms of PN. Mathematics of Computation, 84:291 (2015), 289-308.
[Huy2005]D. Huybrechts : Complex Geometry, Springer (Berlin) (2005).


[IK2010]Kenji Iohara and Yoshiyuki Koga. Representation Theory of the Virasoro Algebra. Springer, (2010).
[ILS2012]Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni. Finding strong bridges and strong articulation points in linear time. Theoretical Computer Science, 447, 74–84 (2012). doi:10.1016/j.tcs.2011.11.011
[IR1990]K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, GTM volume 84, 1990.
[ISSK2009]M. Izadi, B. Sadeghiyan, S. S. Sadeghian, H. A. Khanooki, MIBS: A new lightweight block cipher; in CANS, (2009), pp. 334-348.
[Iwa1964]N. Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. I, 10 (1964), 215–236 (1964). MathSciNet MR0165016
[Iwa1972]K. Iwasawa, Lectures on p-adic L-functions, Princeton University Press, 1972.


[Ja1971]N. Jacobson. Exceptional Lie Algebras. Marcel Dekker, Inc. New York. 1971. IBSN No. 0-8247-1326-5.
[JL2009]Nicolas Jacon and Cedric Lecouvey. Kashiwara and Zelevinsky involutions in affine type A. Pac. J. Math. 243(2):287-311 (2009).
[Joh1990]D.L. Johnson. Presentations of Groups. Cambridge University Press. (1990).
[Jon1987]V. Jones, Hecke algebra representations of braid groups and link polynomials. Ann. of Math. (2) 126 (1987), no. 2, 335–388. doi:10.2307/1971403 MathSciNet MR0908150
[Jon2005]V. Jones, The Jones Polynomial, 2005.
[JRJ94]Jourdan, Guy-Vincent; Rampon, Jean-Xavier; Jard, Claude (1994), “Computing on-line the lattice of maximal antichains of posets”, Order 11 (3) p. 197-210, doi:10.1007/BF02115811
[Joy2004]D. Joyner, Toric codes over finite fields, Applicable Algebra in Engineering, Communication and Computing, 15, (2004), p. 63-79.
[Joy2006]D. Joyner, On quadratic residue codes and hyperelliptic curves, (preprint 2006)
[JPdA15]N. Jacon and L. Poulain d’Andecy. An isomorphism theorem for Yokonuma-Hecke algebras and applications to link invariants. (2015) Arxiv 1501.06389v3.


[Ka1990]Victor G. Kac. Infinite-dimensional Lie Algebras. Third edition. Cambridge University Press, Cambridge, 1990.
[Kal1992]B. Kaliski, The MD2 message-digest algorithm; in RFS 1319, (1992).
[Ka1993]Masaki Kashiwara, The crystal base and Littelmann’s refined Demazure character formula, Duke Math. J. 71 (1993), no. 3, 839–858.
[Kal1980]T. Kaliath, “Linear Systems”, Prentice-Hall, 1980, 383–386.
[Kam2007]Joel Kamnitzer, The crystal structure on the set of Mirković-Vilonen polytopes, Adv. Math. 215 (2007), 66-93.
[Kam2010]Joel Kamnitzer, Mirković-Vilonen cycles and polytopes, Ann. Math. (2) 171 (2010), 731-777.
[Kan1958]D. M. Kan, A combinatorial definition of homotopy groups, Ann. Math. (2) 67 (1958), 282-312.
[Kat1991]Nicholas M. Katz, Exponential sums and differential equations, Princeton University Press, Princeton NJ, 1991.
[Kaw2009]Kawahira, Tomoki. An algorithm to draw external rays of the Mandelbrot set, Nagoya University, 23 Apr. 2009.
[KB1983]W. Kühnel and T. F. Banchoff, “The 9-vertex complex projective plane”, Math. Intelligencer 5 (1983), no. 3, 11-22.
[Ke1991]A. Kerber. Algebraic combinatorics via finite group actions, 2.2 p. 70. BI-Wissenschaftsverlag, Mannheim, 1991.
[Ke2008]B. Keller, Cluster algebras, quiver representations and triangulated categories, Arxiv 0807.1960.
[KK1995]Victor Klee and Peter Kleinschmidt, Convex polytopes and related complexes., in R. L. Graham, M. Grötschel, L Lovász, Handbook of combinatorics, Vol. 1, Chapter 18, 1995
[KKMMNN1992]S-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki. Affine crystals and vertex models. Int. J. Mod. Phys. A, 7 (suppl. 1A), (1992) pp. 449-484.
[KKPSSSYYLLCHH2004]D. Kwon, J. Kim, S. Park, S. H. Sung, Y. Sohn, J. H. Song, Y. Yeom, E-J. Yoon, S. Lee, J. Lee, S. Chee, D. Han, and J. Hong, New block cipher: ARIA; in ICISC, (2004), pp. 432-445.
[KL1990]P. Kleidman and M. Liebeck. The subgroup structure of the finite classical groups. Cambridge University Press, 1990.
[KL2008]Chris Kurth and Ling Long, “Computations with finite index subgroups of \({\rm PSL}_2(\ZZ)\) using Farey symbols”, Advances in algebra and combinatorics, 225–242, World Sci. Publ., Hackensack, NJ, 2008. Preprint version: Arxiv 0710.1835
[KLLRSY2014]E. B. Kavun, M. M. Lauridsen, G. Leander, C. Rechberger, P. Schwabe, and T. Yalcin, Prost v1; CAESAR Competition, (2014).
[KLPR2010]L. R. Knudsen, G. Leander, A. Poschmann, and M. J. B. Robshaw, PRINTcipher: A block cipher for IC-printing; in CHES, (2010), pp. 16-32.
[KLS2013]Allen Knutson, Thomas Lam, and David Speyer. Positroid Varieties: Juggling and Geometry Compositio Mathematica, 149 (2013), no. 10. Arxiv 1111.3660.
[KMAUTOM2000]Masayuki Kanda, Shiho Moriai, Kazumaro Aoki, Hiroki Ueda, Youichi Takashima, Kazuo Ohta, and Tsutomu Matsumoto, E2 - a new 128-bit block cipher; in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E83-A(1):48–59, 12 2000.
[KMM2004]Tomasz Kaczynski, Konstantin Mischaikow, and Marian Mrozek, “Computational Homology”, Springer-Verlag (2004).
[KMN2012]On the trace of the antipode and higher indicators. Yevgenia Kashina and Susan Montgomery and Richard Ng. Israel J. Math., v.188, 2012.
[KN1963]S. Kobayashi & K. Nomizu : Foundations of Differential Geometry, vol. 1, Interscience Publishers (New York) (1963).
[KNS2011]Atsuo Kuniba and Tomoki Nakanishi and Junji Suzuki, \(T\)-systems and \(Y\)-systems in integrable systems. J. Phys. A, 44 (2011), no. 10.
[KnotAtlas]The Knot atlas.
[Knu1995]Donald E. Knuth, Overlapping Pfaffians, Arxiv math/9503234v1.
[Knu2005]Lars R. Knudsen, SMASH - A Cryptographic Hash Function; in FSE‘05, (2005), pp. 228-242.
[Kob1993]Neal Koblitz, Introduction to Elliptic Curves and Modular Forms. Springer GTM 97, 1993.
[Koe1999]Wolfram Koepf: Effcient Computation of Chebyshev Polynomials in Computer Algebra Systems: A Practical Guide. John Wiley, Chichester (1999): 79-99.
[Koh2000]David Kohel, Hecke Module Structure of Quaternions, in Class Field Theory — Its Centenary and Prospect (Tokyo, 1998), Advanced Studies in Pure Mathematics, 30, 177-196, 2000.
[Koh2007]A. Kohnert, Constructing two-weight codes with prescribed groups of automorphisms, Discrete applied mathematics 155, no. 11 (2007): 1451-1457.
[Kos1985]J.-L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, in Élie Cartan et les mathématiques d’aujourd’hui, Astérisque hors série (1985), p. 257
[KP2002]Volker Kaibel and Marc E. Pfetsch, “Computing the Face Lattice of a Polytope from its Vertex-Facet Incidences”, Computational Geometry: Theory and Applications, Volume 23, Issue 3 (November 2002), 281-290. Available at and free of charge at Arxiv math/0106043
[Kra2006]Christian Krattenthaler. Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes. Advances in Applied Mathematics Volume 37, Number 3 (2006), pp. 404-431.
[Kr1971]D. Kraines, “On excess in the Milnor basis,” Bull. London Math. Soc. 3 (1971), 363-365.
[Kr2016]Stefan Kranich, An epsilon-delta bound for plane algebraic curves and its use for certified homotopy continuation of systems of plane algebraic curves, Arxiv 1505.03432
[KR2001]J. Kahane and A. Ryba. The hexad game, Electronic Journal of Combinatorics, 8 (2001).
[KS1998]Maximilian Kreuzer and Harald Skarke, Classification of Reflexive Polyhedra in Three Dimensions, Arxiv hep-th/9805190
[KS2002]A. Khare and U. Sukhatme. “Cyclic Identities Involving Jacobi Elliptic Functions”, preprint 2002. Arxiv math-ph/0201004
[KSV2011]Ian Kiming, Matthias Schuett and Helena Verrill, “Lifts of projective congruence groups”, J. London Math. Soc. (2011) 83 (1): 96-120, doi:10.1112/jlms/jdq062. Arxiv version: Arxiv 0905.4798.
[KT1986]N. Kerzman and M. R. Trummer. “Numerical Conformal Mapping via the Szego kernel”. Journal of Computational and Applied Mathematics, 14(1-2): 111–123, 1986.
[Kuh1987]W. Kühnel, “Minimal triangulations of Kummer varieties”, Abh. Math. Sem. Univ. Hamburg 57 (1987), 7-20.
[Kuh1995]Kuhnel, “Tight Polyhedral Submanifolds and Tight Triangulations” Lecture Notes in Mathematics Volume 1612, 1995
[Kul1991]Ravi Kulkarni, “An arithmetic geometric method in the study of the subgroups of the modular group”, American Journal of Mathematics 113 (1991), no 6, 1053-1133
[Kur2008]Chris Kurth, “K Farey package for Sage”,
[Kwon2012]Jae-Hoon Kwon. Crystal bases of \(q\)-deformed Kac Modules over the Quantum Superalgebra \(U_q(\mathfrak{gl}(m|n))\). International Mathematics Research Notices. Vol. 2014, No. 2, pp. 512-550 (2012)
[KZ2003]M. Kontsevich, A. Zorich “Connected components of the moduli space of Abelian differentials with prescripebd singularities” Invent. math. 153, 631-678 (2003)


[Lam2004]Thomas Lam, Growth diagrams, domino insertion and sign-imbalance. Journal of Combinatorial Theory, Series A Volume 107, Number 1 (2004), pp. 87-115.
[Lam2005]T. Lam, Affine Stanley symmetric functions, Amer. J. Math. 128 (2006), no. 6, 1553–1586.
[Lam2008]T. Lam. Schubert polynomials for the affine Grassmannian. J. Amer. Math. Soc., 2008.
[Lan2002]S. Lang : Algebra, 3rd ed., Springer (New York) (2002); doi:10.1007/978-1-4613-0041-0
[Lan2008]E. Lanneau “Connected components of the strata of the moduli spaces of quadratic differentials”, Annales sci. de l’ENS, serie 4, fascicule 1, 41, 1-56 (2008)
[Lau2011]Alan G.B. Lauder, “Computations with classical and p-adic modular forms”, LMS J. of Comput. Math. 14 (2011), 214-231.
[LB1988]Lee, P.J., Brickell, E.F. An observation on the security of McEliece’s public-key cryptosystem. EuroCrypt 1988. LNCS, vol. 330, pp. 275–280.
[LdB1982]A. Liberato de Brito, ‘FORTRAN program for the integral of three spherical harmonics’, Comput. Phys. Commun., Volume 25, pp. 81-85 (1982)
[Lee1996]Marc van Leeuwen. The Robinson-Schensted and Sch”utzenberger algorithms, an elementary approach. Electronic Journal of Combinatorics 3, no. 2 (1996): Research Paper 15, approx. 32 pp. (electronic)
[Lee1997]J. M. Lee, Riemannian Manifolds, Springer (New York) (1997); doi:10.1007/b98852
[Lee2011]J. M. Lee, Introduction to Topological Manifolds, 2nd ed., Springer (New York) (2011); doi:10.1007/978-1-4419-7940-7
[Lee2013]J. M. Lee, Introduction to Smooth Manifolds, 2nd ed., Springer (New York) (2013); doi:10.1007/978-1-4419-9982-5
[Lev2014]Lionel Levine. Threshold state and a conjecture of Poghosyan, Poghosyan, Priezzhev and Ruelle, Communications in Mathematical Physics.
[Lew2000]Robert Edward Lewand. Cryptological Mathematics. The Mathematical Association of America, 2000.
[Li1995]Peter Littelmann, Crystal graphs and Young tableaux, J. Algebra 175 (1995), no. 1, 65–87.
[Lic1977]A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, Journal of Differential Geometry 12, 253 (1977); doi:10.4310/jdg/1214433987
[Lic1997]William B. Raymond Lickorish. An Introduction to Knot Theory, volume 175 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1997. ISBN 0-387-98254-X
[Lim]C. H. Lim, CRYPTON: A New 128-bit Block Cipher; available at
[Lim2001]C. H. Lim, A Revised Version of CRYPTON: CRYPTON V1.0; in FSE‘01, pp. 31–45.
[Lin1999]J. van Lint, Introduction to coding theory, 3rd ed., Springer-Verlag GTM, 86, 1999.
[Liv2006]M. Livernet, A rigidity theorem for pre-Lie algebras, J. Pure Appl. Algebra 207 (2006), no 1, pages 1-18. Preprint: Arxiv math/0504296v2.
[LLYCL2005]H. J. Lee, S. J. Lee, J. H. Yoon, D. H. Cheon, and J. I. Lee, The SEED Encryption Algorithm; in RFC 4269, (2005).
[LLZ2014]K. Lee, L. Li, and A. Zelevinsky, Greedy elements in rank 2 cluster algebras, Selecta Math. 20 (2014), 57-82.
[LLMSSZ2013]Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono and Mike Zabrocki. k-Schur functions and affine Schubert calculus. Arxiv 1301.3569.
[LM2006]Vadim Lyubashevsky and Daniele Micciancio. Generalized compact knapsacks are collision resistant. ICALP, pp. 144–155, Springer, 2006.
[LMR2010]N. Linial, R. Meshulam and M. Rosenthal, “Sum complexes – a new family of hypertrees”, Discrete & Computational Geometry, 2010, Volume 44, Number 3, Pages 622-636
[Lod1995]Jean-Louis Loday. Cup-product for Leibniz cohomology and dual Leibniz algebras. Math. Scand., pp. 189–196 (1995).
[Loe2007]David Loeffler, Spectral expansions of overconvergent modular functions, Int. Math. Res. Not 2007 (050). Arxiv math/0701168.
[Lot2005]M. Lothaire, Applied combinatorics on words. Cambridge University Press (2005).
[LP2007]G. Leander and A. Poschmann, On the Classification of 4 Bit S-boxes; in WAIFI, (2007), pp. 159-176.
[LP2011]Richard Lindner and Chris Peikert. Better key sizes (and attacks) for LWE-based encryption. in Proceeding of the 11th international conference on Topics in cryptology: CT-RSA 2011. Springer 2011, doi:10.1007/978-3-642-19074-2_21
[LPR2010]Vadim Lyubashevsky, Chris Peikert, and Oded Regev. On Ideal Lattices and Learning with Errors over Rings. in Advances in Cryptology – EUROCRYPT 2010. Springer 2010. doi:10.1007/978-3-642-13190-5_1
[LS2007]Thomas Lam and Mark Shimozono. Dual graded graphs for Kac-Moody algebras. Algebra & Number Theory 1.4 (2007) pp. 451-488.
[LSS2009]T. Lam, A. Schilling, M. Shimozono. Schubert polynomials for the affine Grassmannian of the symplectic group. Mathematische Zeitschrift 264(4) (2010) 765-811 (Arxiv 0710.2720)
[LS2017]Xuan Liu and Travis Scrimshaw. A uniform approach to soliton cellular automata using rigged configurations. Preprint (2017) Arxiv 1706.02443
[LT1998]B. Leclerc, J.-Y. Thibon, Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials,
[LT2009]G. I. Lehrer and D. E. Taylor. Unitary reflection groups. Australian Mathematical Society Lecture Series, 2009.
[Lut2002]Frank H. Lutz, Császár’s Torus, Electronic Geometry Model No. 2001.02.069 (2002).
[Lut2005]Frank H. Lutz, “Triangulated Manifolds with Few Vertices: Combinatorial Manifolds”, preprint (2005), Arxiv math/0506372
[LV2012]Jean-Louis Loday and Bruno Vallette. Algebraic Operads. Springer-Verlag Berlin Heidelberg (2012). doi:10.1007/978-3-642-30362-3.
[Ltd06]Beijing Data Security Technology Co. Ltd, Specification of SMS4, Block Cipher for WLAN Products - SMS4 (in Chinese); Available at, (2006).
[LTV1999]Bernard Leclerc, Jean-Yves Thibon, and Eric Vasserot. Zelevinsky’s involution at roots of unity. J. Reine Angew. Math. 513:33-51 (1999).
[LW2012]David Loeffler and Jared Weinstein, On the computation of local components of a newform, Mathematics of Computation 81 (2012) 1179-1200. doi:10.1090/S0025-5718-2011-02530-5
[Lyo2003]R. Lyons, Determinantal probability measures. Publications Mathematiques de l’Institut des Hautes Etudes Scientifiques 98(1) (2003), pp. 167-212.


[Mac1987]Maciej M. SysŁo, Minimizing the jump number for partially-ordered sets: a graph-theoretic approach, II. Discrete Mathematics, Volume 63, Issues 2-3, 1987, Pages 279-295.
[MagmaHGM]Hypergeometric motives in Magma,
[Mas94]James L. Massey, SAFER K-64: A byte-oriented block-ciphering algorithm; in FSE’93, Volume 809 of LNCS, pages 1-17. Springer, Heidelberg, December 1994.
[Mat1992]O. Mathieu. Classification of Harish-Chandra modules over the Virasoro Lie algebra. Invent. Math. 107(2) (1992), pp. 225-234.
[Mat2002]Jiří Matousek, “Lectures on Discrete Geometry”, Springer, 2002
[Ma2009]Sarah Mason, An Explicit Construction of Type A Demazure Atoms, Journal of Algebraic Combinatorics, Vol. 29, (2009), No. 3, p.295-313. Arxiv 0707.4267
[Mac1936I]Saunders MacLane, A construction for prime ideals as absolute values of an algebraic field. Duke Mathematical Journal, 2(3) (1936), 492-510.
[Mac1936II]Saunders MacLane, A construction for absolute values in polynomial rings. Transactions of the American Mathematical Society, 40(3)(1936), 363-395.
[Mac1915]Percy A. MacMahon, Combinatory Analysis, Cambridge University Press (1915–1916). (Reprinted: Chelsea, New York, 1960).
[MAR2009]H. Molina-Abril and P. Réal, Homology computation using spanning trees in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, Lecture Notes in Computer Science, volume 5856, pp 272-278, Springer, Berlin (2009).
[Mar1997]C.-M. Marle, The Schouten-Nijenhuis bracket and interior products, Journal of Geometry and Physics 23, 350 (1997); doi:10.1016/S0393-0440(97)80009-5
[Mas1969]James L. Massey, “Shift-Register Synthesis and BCH Decoding.” IEEE Trans. on Information Theory, vol. 15(1), pp. 122-127, Jan 1969.
[MatroidDatabase]Database of Matroids
[May1964]J. P. May, “The cohomology of restricted Lie algebras and of Hopf algebras; application to the Steenrod algebra.” Thesis, Princeton Univ., 1964.
[May1967]J. P. May, Simplicial Objects in Algebraic Topology, University of Chicago Press (1967)
[McC1978]K. McCrimmon. Jordan algebras and their applications. Bull. Amer. Math. Soc. 84 1978.
[McM1992]John McMillan. Games, strategies, and managers. Oxford University Press.
[Mil1958]J. W. Milnor, “The Steenrod algebra and its dual,” Ann. of Math. (2) 67 (1958), 150-171.
[MirMor2009]R. Miranda, D.R. Morrison, “Embeddings of Integral Quadratic Forms” .
[MMIB2012]Y. Matsumoto, S. Moriyama, H. Imai, D. Bremner: Matroid Enumeration for Incidence Geometry, Discrete and Computational Geometry, vol. 47, issue 1, pp. 17-43, 2012.
[MMY2003]Jean-Christophe Yoccoz, Stefano Marmi and Pierre Moussa “On the cohomological equation for interval exchange maps”, C. R. Acad. Sci. Paris, projet de Note, 2003 Systèmes dynamiques/Dynamical Systems. Arxiv math/0304469v1
[MM2015]J. Matherne and G. Muller, Computing upper cluster algebras, Int. Math. Res. Not. IMRN, 2015, 3121-3149.
[MNO1994]Alexander Molev, Maxim Nazarov, and Grigori Olshanski. Yangians and classical Lie algebras. (1994) Arxiv hep-th/9409025
[Mol2007]Alexander Ivanovich Molev. Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society. (2007)
[Mol2015]A. Molnar, Fractional Linear Minimal Models of Rational Functions, M.Sc. Thesis.
[Mon1998]K. G. Monks, “Change of basis, monomial relations, and \(P^s_t\) bases for the Steenrod algebra,” J. Pure Appl. Algebra 125 (1998), no. 1-3, 235-260.
[MoPa1994]P. Morton and P. Patel. The Galois theory of periodic points of polynomial maps. Proc. London Math. Soc., 68 (1994), 225-263.
[MR1989]G. Melançon and C. Reutenauer. Lyndon words, free algebras and shuffles, Can. J. Math., Vol. XLI, No. 4, 1989, pp. 577-591.
[MR2002]S. Murphy, M. Robshaw Essential Algebraic Structure Within the AES; in Advances in Cryptology - CRYPTO 2002; LNCS 2442; Springer Verlag 2002
[MS2003]T. Mulders, A. Storjohann, “On lattice reduction for polynomial matrices”, J. Symbolic Comput. 35 (2003), no. 4, 377–401
[MS2011]G. Musiker and C. Stump, A compendium on the cluster algebra and quiver package in sage, Arxiv 1102.4844.
[MSZ2013]Michael Maschler, Solan Eilon, and Zamir Shmuel. Game Theory. Cambridge: Cambridge University Press, (2013). ISBN 9781107005488.
[Mu1997]Murty, M. Ram. Congruences between modular forms. In “Analytic Number Theory” (ed. Y. Motohashi), London Math. Soc. Lecture Notes 247 (1997), 313-320, Cambridge Univ. Press.
[MV2010]D. Micciancio, P. Voulgaris. A Deterministic Single Exponential Time Algorithm for Most Lattice Problems based on Voronoi Cell Computations. Proceedings of the 42nd ACM Symposium Theory of Computation, 2010.
[MvOV1996]A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1996.
[MW2009]Meshulam and Wallach, “Homological connectivity of random \(k\)-dimensional complexes”, preprint, math.CO/0609773.


[Nas1950]John Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36.1 (1950): 48-49.
[Nie2013]Johan S. R. Nielsen, List Decoding of Algebraic Codes, Ph.D. Thesis, Technical University of Denmark, 2013
[Nie]Johan S. R. Nielsen, Codinglib,
[Nij1955]A. Nijenhuis, Jacobi-type identities for bilinear differential concomitants of certain tensor fields. I, Indagationes Mathematicae (Proceedings) 58, 390 (1955).
[NN2007]Nisan, Noam, et al., eds. Algorithmic game theory. Cambridge University Press, 2007.
[Nog1985]Arnaldo Nogueira, “Almost all Interval Exchange Transformations with Flips are Nonergodic” (Ergod. Th. & Dyn. Systems, Vol 5., (1985), 257-271
[Normaliz]Winfried Bruns, Bogdan Ichim, and Christof Soeger, Normaliz,
[NZ2012]T. Nakanishi and A. Zelevinsky, On tropical dualities in cluster algebras, Algebraic groups and quantum groups, Contemp. Math., vol. 565, Amer. Math. Soc., Providence, RI, 2012, pp. 217-226.
[Nze2007]Janvier Nzeutchap. Binary Search Tree insertion, the Hypoplactic insertion, and Dual Graded Graphs. Arxiv 0705.2689 (2007).


[OGKRKGBDDP2015]R. Oliynykov, I. Gorbenko, O. Kazymyrov, V. Ruzhentsev, O. Kuznetsov, Y. Gorbenko, A. Boiko, O. Dyrda, V. Dolgov, and A. Pushkaryov, A new standard of ukraine: The kupyna hash function; in Cryptology ePrint Archive, (2015), 885.
[Oha2011]R.A. Ohana. On Prime Counting in Abelian Number Fields.
[ONe1983]B. O’Neill : Semi-Riemannian Geometry, Academic Press (San Diego) (1983)
[Or2016]M. Orlitzky. The Lyapunov rank of an improper cone. Citation: Optimization Methods and Software (accepted 2016-06-12). doi:10.1080/10556788.2016.1202246
[Oxl1992]James Oxley, Matroid theory, Oxford University Press, 1992.
[Oxl2011]James Oxley, Matroid Theory, Second Edition. Oxford University Press, 2011.


[PALP]Maximilian Kreuzer, Harald Skarke: “PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry” omput.Phys.Commun. 157 (2004) 87-106 Arxiv math/0204356
[Pana2002]F. Panaite, Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees, Lett. Math. Phys. 51 (2000), no. 3, pages 211-219. Preprint: Arxiv math/0003074v1
[PearsonTest]Wikipedia article Goodness_of_fit, accessed 13th October 2009.
[Pen2012]R. Pendavingh, On the evaluation at \((-i, i)\) of the Tutte polynomial of a binary matroid. Preprint: Arxiv 1203.0910
[Pet2010]Christiane Peters, Information-set decoding for linear codes over \(GF(q)\), Proc. of PQCrypto 2010, pp. 81-94.
[Pha2002]R. C.-W. Phan. Mini advanced encryption standard (mini-AES): a testbed for cryptanalysis students. Cryptologia, 26(4):283–306, 2002.
[Piz1980]A. Pizer. An Algorithm for Computing Modular Forms on \(\Gamma_0(N)\), J. Algebra 64 (1980), 340-390.
[Platt1976]C. R. Platt, Planar lattices and planar graphs, Journal of Combinatorial Theory Series B, Vol 21, no. 1 (1976): 30-39.
[Pon2010]S. Pon. Types B and D affine Stanley symmetric functions, unpublished PhD Thesis, UC Davis, 2010.
[Pos2005]A. Postnikov, Affine approach to quantum Schubert calculus, Duke Math. J. 128 (2005) 473-509
[PPW2013]D. Perkinson, J. Perlman, and J. Wilmes. Primer for the algebraic geometry of sandpiles. Tropical and Non-Archimedean Geometry, Contemp. Math., 605, Amer. Math. Soc., Providence, RI, 2013. Arxiv 1112.6163
[PR2015]P. Pilarczyk and P. Réal, Computation of cubical homology, cohomology, and (co)homological operations via chain contraction, Adv. Comput. Math. 41 (2015), pp 253–275.
[PRC2012]G. Piret, T. Roche, and C. Carlet, PICARO - a block cipher allowing efficient higher-order side-channel resistance; in ACNS, (2012), pp. 311-328.
[Prototype_pattern]Prototype pattern, Wikipedia article Prototype_pattern
[PS2011]R. Pollack, and G. Stevens. Overconvergent modular symbols and p-adic L-functions. Annales scientifiques de l’Ecole normale superieure. Vol. 44. No. 1. Elsevier, 2011.
[PUNTOS]Jesus A. De Loera
[PvZ2010]R. A. Pendavingh, S. H. M. van Zwam, Lifts of matroid representations over partial fields, Journal of Combinatorial Theory, Series B, Volume 100, Issue 1, January 2010, Pages 36-67
[PZ2008]J. H. Palmieri and J. J. Zhang, “Commutators in the Steenrod algebra,” New York J. Math. 19 (2013), 23-37.
[Propp1997]James Propp, Generating Random Elements of Finite Distributive Lattices, Electron. J. Combin. 4 (1997), no. 2, The Wilf Festschrift volume, Research Paper 15.


[Raj1987]A. Rajan, Algorithmic applications of connectivity and related topics in matroid theory. Ph.D. Thesis, Northwestern university, 1987.
[Rau1979]Gerard Rauzy, “Echanges d’intervalles et transformations induites”, Acta Arith. 34, no. 3, 203-212, 1980
[Red2001]Maria Julia Redondo. Hochschild cohomology: some methods for computations. Resenhas IME-USP 5 (2), 113-137 (2001).
[Reg09]Oded Regev. On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. in Journal of the ACM 56(6). ACM 2009, doi:10.1145/1060590.1060603
[Reg1958]T. Regge, ‘Symmetry Properties of Clebsch-Gordan Coefficients’, Nuovo Cimento, Volume 10, pp. 544 (1958)
[Reg1959]T. Regge, ‘Symmetry Properties of Racah Coefficients’, Nuovo Cimento, Volume 11, pp. 116 (1959)
[Reg2005]Oded Regev. On lattices, learning with errors, random linear codes, and cryptography. STOC, pp. 84–93, ACM, 2005.
[Reu1993]C. Reutenauer. Free Lie Algebras. Number 7 in London Math. Soc. Monogr. (N.S.). Oxford University Press. (1993).
[Rho69]John Rhodes, Characters and complexity of finite semigroups J. Combinatorial Theory, vol 6, 1969
[RH2003]J. Rasch and A. C. H. Yu, ‘Efficient Storage Scheme for Pre-calculated Wigner 3j, 6j and Gaunt Coefficients’, SIAM J. Sci. Comput. Volume 25, Issue 4, pp. 1416-1428 (2003)
[RH2003b]G. G. Rose and P. Hawkes, Turing: A fast stream cipher; in FSE, (2003), pp. 290-306.
[Rio1958]J. Riordan, “An Introduction to Combinatorial Analysis”, Dover Publ. (1958)
[Ris2016]Roswitha Rissner, “Null ideals of matrices over residue class rings of principal ideal domains”. Linear Algebra Appl., 494 (2016) 44–69. doi:10.1016/j.laa.2016.01.004.
[RMA2009]P. Réal and H. Molina-Abril, Cell AT-models for digital volumes in Torsello, Escolano, Brun (eds.), Graph-Based Representations in Pattern Recognition, Lecture Notes in Computer Science, volume 5534, pp. 314-3232, Springer, Berlin (2009).
[RNPA2011]G. Rudolf, N. Noyan, D. Papp, and F. Alizadeh. Bilinear optimality constraints for the cone of positive polynomials. Mathematical Programming, Series B, 129 (2011) 5-31.
[Rob1991]Tom Roby, “Applications and extensions of Fomin’s generalization of the Robinson-Schensted correspondence to differential posets”. Ph.D. Thesis, M.I.T., Cambridge, Massachusetts, 1991.
[Roberts2015]David P. Roberts, Hypergeometric Motives I,,_I_]_David_Roberts,_University_of_Minnesota_-_Morris.pdf
[Roberts2017]David P. Roberts, Hypergeometric motives and an unusual application of the Guinand-Weil-Mestre explicit formula,
[Roc1970]R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton, 1970.
[Ros1999]K. Rosen Handbook of Discrete and Combinatorial Mathematics (1999), Chapman and Hall.
[Rot2001]Gunter Rote, Division-Free Algorithms for the Determinant and the Pfaffian: Algebraic and Combinatorial Approaches, H. Alt (Ed.): Computational Discrete Mathematics, LNCS 2122, pp. 119–135, 2001.
[Rot2006]Ron Roth, Introduction to Coding Theory, Cambridge University Press, 2006
[RSS]Wikipedia article Residual_sum_of_squares, accessed 13th October 2009.
[Rud1958]M. E. Rudin. An unshellable triangulation of a tetrahedron. Bull. Amer. Math. Soc. 64 (1958), 90-91.
[Rüt2014]Julian Rüth, Models of Curves and Valuations. Open Access Repositorium der Universität Ulm. Dissertation (2014). doi:10.18725/OPARU-3275


[Saa2011]M-J. O. Saarinen, Cryptographic Analysis of All 4 x 4-Bit S-Boxes; in SAC, (2011), pp. 118-133.
[Sag1987]Bruce E. Sagan. Shifted tableaux, Schur Q-functions, and a conjecture of R. Stanley. Journal of Combinatorial Theory, Series A Volume 45 (1987), pp. 62-103.
[Sch1996]E. Schaefer. A simplified data encryption algorithm. Cryptologia, 20(1):77–84, 1996.
[Sch2006]Oliver Schiffmann. Lectures on Hall algebras, preprint, 2006. Arxiv 0611617v2.
[Sch2015]George Schaeffer. Hecke stability and weight 1 modular forms. Math. Z. 281:159–191, 2015. doi:10.1007/s00209-015-1477-9
[Sco1985]R. Scott, Wide-open encryption design offers flexible implementations; in Cryptologia, (1985), pp. 75-91.
[SE1962]N. E. Steenrod and D. B. A. Epstein, Cohomology operations, Ann. of Math. Stud. 50 (Princeton University Press, 1962).
[Ser1992]J.-P. Serre : Lie Algebras and Lie Groups, 2nd ed., Springer (Berlin) (1992); doi:10.1007/978-3-540-70634-2
[Ser2010]F. Sergeraert, Triangulations of complex projective spaces in Scientific contributions in honor of Mirian Andrés Gómez, pp 507-519, Univ. La Rioja Serv. Publ., Logroño (2010).
[Sey1981]P. D. Seymour, Nowhere-zero 6-flows, J. Comb. Theory Ser B, 30 (1981), 130-135. :doi: \(10.1016/0095-8956(81)90058-7\)
[SH1995]C. P. Schnorr and H. H. Hörner. Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction. Advances in Cryptology - EUROCRYPT ‘95. LNCS Volume 921, 1995, pp 1-12.
[Shi1971]Goro Shimura, Introduction to the arithmetic theory of automorphic functions. Publications of the Mathematical Society of Japan and Princeton University Press, 1971.
[Shr2004]S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer, 2004
[SIHMAS2011]K. Shibutani, T. Isobe, H. Hiwatari, A. Mitsuda, T. Akishita, and T. Shirai, Piccolo: An ultra-lightweight block-cipher; in CHES, (2011), pp. 342-457.
[Sil1994]Joseph H. Silverman, Advanced topics in the arithmetic of elliptic curves. GTM 151, Springer-Verlag, New York, 1994.
[Sil2007]Joseph H. Silverman. The Arithmetic of Dynamics Systems. GTM 241, Springer-Verlag, New York, 2007.
[SK2011]J. Spreer and W. Kühnel, “Combinatorial properties of the K3 surface: Simplicial blowups and slicings”, Experimental Mathematics, Volume 20, Issue 2, 2011.
[SKWWHF1998]B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall, and N. Ferguson, Twofish: A 128-bit block cipher; in AES Submission, (1998).
[Sky2003]Brian Skyrms. The stag hunt and the evolution of social structure. Cambridge University Press, 2003.
[SLB2008]Shoham, Yoav, and Kevin Leyton-Brown. Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press, 2008.
[SMMK2013]T. Suzaki, K. Minematsu, S. Morioka, and E. Kobayashi, TWINE: A lightweight block cipher for multiple platforms; in SAC, (2012), pp. 338-354.
[Sor1984]A. Sorkin, LUCIFER: a cryptographic algorithm; in Cryptologia, 8(1), pp. 22–35, 1984.
[Spa1966]Edwin H. Spanier, Algebraic Topology, Springer-Verlag New York, 1966. doi:10.1007/978-1-4684-9322-1, ISBN 978-1-4684-9322-1.
[Spe2013]D. Speyer, An infinitely generated upper cluster algebra, Arxiv 1305.6867.
[SPGQ2006]F.-X. Standaert, G. Piret, N. Gershenfeld, and J.-J. Quisquater, Sea: A scalable encryption algorithm for small embedded applications; in CARDIS, (2006), pp. 222-236.
[SPRQL2004]F.-X. Standaert, G. Piret, G. Rouvroy, J.-J. Quisquarter, and J.-D. Legat, ICEBERG: An involutional cipher efficient for block encryption in reconfigurable hardware; in FSE, (2004), pp. 279-299.
[SS1990]Bruce E. Sagan and Richard P. Stanley. Robinson-Schensted algorithms for skew tableaux. Journal of Combinatorial Theory, Series A 55.2 (1990) pp. 161-193.
[SS1992]M. A. Shtan’ko and M. I. Shtogrin, “Embedding cubic manifolds and complexes into a cubic lattice”, Uspekhi Mat. Nauk 47 (1992), 219-220.
[SS2015]Anne Schilling and Travis Scrimshaw. Crystal structure on rigged configurations and the filling map. Electron. J. Combin., 22(1) (2015) #P1.73. Arxiv 1409.2920.
[SS2015II]Ben Salisbury and Travis Scrimshaw. A rigged configuration model for \(B(\infty)\). J. Combin. Theory Ser. A, 133 (2015) pp. 29-75. Arxiv 1404.6539.
[SS2017]Ben Salisbury and Travis Scrimshaw. Rigged configurations for all symmetrizable types. Electron. J. Combin., 24(1) (2017) #P1.30. Arxiv 1509.07833.
[SSAMI2007]T. Shirai, K. Shibutani, T. Akishita, S. Moriai, and T. Iwata, The 128-bit blockcipher CLEFIA (extended abstract); in FSE, (2007), pp. 181-195.
[ST2011]A. Schilling, P. Tingley. Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function. Electronic Journal of Combinatorics. 19(2). 2012. Arxiv 1104.2359
[St1986]Richard Stanley. Two poset polytopes, Discrete Comput. Geom. (1986), doi:10.1007/BF02187680
[Sta2007]Stanley, Richard: Hyperplane Arrangements, Geometric Combinatorics (E. Miller, V. Reiner, and B. Sturmfels, eds.), IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, Providence, RI, 2007, pp. 389-496.
[EnumComb1]Stanley, Richard P. Enumerative Combinatorics, volume 1, Second Edition, Cambridge University Press (2011).
[Stan2009]Richard Stanley, Promotion and evacuation, Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Björner, Research Paper 9, 24 pp.
[Ste2003]John R. Stembridge, A local characterization of simply-laced crystals, Transactions of the American Mathematical Society, Vol. 355, No. 12 (Dec., 2003), pp. 4807–4823
[Sti2006]Douglas R. Stinson. Cryptography: Theory and Practice. 3rd edition, Chapman & Hall/CRC, 2006.
[Sto1998]A. Storjohann, An O(n^3) algorithm for Frobenius normal form. Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC‘98), ACM Press, 1998, pp. 101-104.
[Sto2000]A. Storjohann, Algorithms for Matrix Canonical Forms. PhD Thesis. Department of Computer Science, Swiss Federal Institute of Technology – ETH, 2000.
[Sto2011]A. Storjohann, Email Communication. 30 May 2011.
[Str1969]Volker Strassen. Gaussian elimination is not optimal. Numerische Mathematik, 13:354-356, 1969.
[Striker2011]J. Striker. A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux, Advances in Applied Mathematics 46 (2011), no. 4, 583-609. Arxiv 1408.5391
[Stu1987]J. Sturm, On the congruence of modular forms, Number theory (New York, 1984-1985), Springer, Berlin, 1987, pp. 275-280.
[Stu1993]B. Sturmfels, Algorithms in invariant theory, Springer-Verlag, 1993.
[STW2013]J. Schejbal, E. Tews, and J. Wälde, Reverse engineering of chiasmus from gstool; in 30c3, (2013).
[STW2016]C. Stump, H. Thomas, N. Williams. Cataland II, in preparation, 2016.
[sudoku:escargot]“Al Escargot”, due to Arto Inkala,
[sudoku:norvig]Perter Norvig, “Solving Every Sudoku Puzzle”,
[sudoku:royle]Gordon Royle, “Minimum Sudoku”,
[sudoku:top95]“95 Hard Puzzles”,, or
[sudoku:wikipedia]“Near worst case”, Wikipedia article Algorithmics_of_sudoku
[SV2000]J. Stern and S. Vaudenay, CS-Cipher; in First Open NESSIE Workshop, (2000).
[SW2002]William Stein and Mark Watkins, A database of elliptic curves—first report. In Algorithmic number theory (ANTS V), Sydney, 2002, Lecture Notes in Computer Science 2369, Springer, 2002, p267–275.
[St1922]Ernst Steinitz, Polyeder und Raumeinteilungen. In Encyclopädie der Mathematischen Wissenschaften, Franz Meyer and Hand Mohrmann, eds., volume 3, Geometrie, erster Teil, zweite Hälfte, pp. 1–139, Teubner, Leipzig, 1922
[Swe1969]Moss Sweedler. Hopf algebras. W.A. Benjamin, Math Lec Note Ser., 1969.
[SWJ2008]Fatima Shaheen, Michael Wooldridge, and Nicholas Jennings. A linear approximation method for the Shapley value. Artificial Intelligence 172.14 (2008): 1673-1699.
[SYYTIYTT2002]T. Shimoyama, H. Yanami, K. Yokoyama, M. Takenaka, K. Itoh, J. Yajima, N. Torii, and H. Tanaka, The block cipher SC2000; in FSE, (2001), pp. 312-327.


[Tar1976]Robert E. Tarjan, Edge-disjoint spanning trees and depth-first search, Acta Informatica 6 (2), 1976, 171-185, doi:10.1007/BF00268499.
[Tate1975]John Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil. Modular functions of one variable, IV, pp. 33–52. Lecture Notes in Math., Vol. 476, Springer, Berlin, 1975.
[Tate1966]John Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. Seminaire Bourbaki, Vol. 9, Exp. No. 306, 1966.
[TB1997]Lloyd N. Trefethen and David Bau III, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
[Tee1997]Tee, Garry J. “Continuous branches of inverses of the 12 Jacobi elliptic functions for real argument”. 1997.
[TIDES]A. Abad, R. Barrio, F. Blesa, M. Rodriguez. TIDES tutorial: Integrating ODEs by using the Taylor Series Method (
[TOPCOM]J. Rambau, TOPCOM <>.
[TW1980]A.D. Thomas and G.V. Wood, Group Tables (Exeter: Shiva Publishing, 1980)


[UDCIKMP2011]M. Ullrich, C. De Canniere, S. Indesteege, Ö. Kücük, N. Mouha, and B. Preenel, Finding Optimal Bitsliced Implementations of 4 x 4-bit S-boxes; in SKEW, (2011).
[UNITTEST]unittest – Unit testing framework –
[U.S1998]U.S. Department Of Commerce/National Institute of Standards and Technology, Skipjack and KEA algorithms specifications, v2.0, (1998).
[U.S1999]U.S. Department Of Commerce/National Institute of Standards and Technology, Data Encryption Standard, (1999).


[Vai1994]I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Springer Basel AG (Basel) (1994); doi:10.1007/978-3-0348-8495-2
[Vat2008]D. Vatne, The mutation class of `D_n` quivers, Arxiv 0810.4789v1.
[VB1996]E. Viterbo, E. Biglieri. Computing the Voronoi Cell of a Lattice: The Diamond-Cutting Algorithm. IEEE Transactions on Information Theory, 1996.
[Vee1978]William Veech, “Interval exchange transformations”, J. Analyse Math. 33 (1978), 222-272
[Ver]Helena Verrill, “Fundamental domain drawer”, Java program,
[Vie1983]Xavier G. Viennot. Maximal chains of subwords and up-down sequences of permutations. Journal of Combinatorial Theory, Series A Volume 34, (1983), pp. 1-14.
[VJ2004]S. Vaudenay and P. Junod, Device and method for encrypting and decryptiong a block of data Fox, a New Family of Block Ciphers, (2004).
[Voe2003]V. Voevodsky, Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes Études Sci. No. 98 (2003), 1-57.
[Voi2012]J. Voight. Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms, to appear.
[VW1994]Leonard Van Wyk. Graph groups are biautomatic. J. Pure Appl. Alg. 94 (1994). no. 3, 341-352.


[Wac2003]Wachs, “Topology of Matching, Chessboard and General Bounded Degree Graph Complexes” (Algebra Universalis Special Issue in Memory of Gian-Carlo Rota, Algebra Universalis, 49 (2003) 345-385)
[Wal1960]C. T. C. Wall, “Generators and relations for the Steenrod algebra,” Ann. of Math. (2) 72 (1960), 429-444.
[Wal1970]David W. Walkup, “The lower bound conjecture for 3- and 4-manifolds”, Acta Math. 125 (1970), 75-107.
[Wan1998]Daqing Wan, “Dimension variation of classical and p-adic modular forms”, Invent. Math. 133, (1998) 449-463.
[Wan2010]Zhenghan Wang. Topological quantum computation. Providence, RI: American Mathematical Society (AMS), 2010. ISBN 978-0-8218-4930-9
[Was1997]L. C. Washington, Cyclotomic Fields, Springer-Verlag, GTM volume 83, 1997.
[Watkins]Mark Watkins, Hypergeometric motives over Q and their L-functions,
[Wat2003]Joel Watson. Strategy: an introduction to game theory. WW Norton, 2002.
[Wat2010]Watkins, David S. Fundamentals of Matrix Computations, Third Edition. Wiley, Hoboken, New Jersey, 2010.
[Web2007]James Webb. Game theory: decisions, interaction and Evolution. Springer Science & Business Media, 2007.
[Weh1998]J. Wehler. Hypersurfaces of the Flag Variety: Deformation Theory and the Theorems of Kodaira-Spencer, Torelli, Lefschetz, M. Noether, and Serre. Math. Z. 198 (1988), 21-38.
[WELLS]Elliot Wells. Computing the Canonical Height of a Point in Projective Space. Arxiv 1602.04920v1 (2016).
[Wei1994]Charles A. Weibel, An introduction to homological algebra. Cambridge Studies in Advanced Math., vol. 38, Cambridge Univ. Press, 1994.
[WFYTP2008]D. Watanable, S. Furuya, H. Yoshida, K. Takaragi, and B. Preneel, A new keystream generator MUGI; in FSE, (2002), pp. 179-194.
[Wil2013]Harold Williams. Q-systems, factorization dynamics, and the twist automorphism. Int. Math. Res. Not. (2015) no. 22, 12042–12069. doi:10.1093/imrn/rnv057.
[Woo1998]R. M. W. Wood, “Problems in the Steenrod algebra,” Bull. London Math. Soc. 30 (1998), no. 5, 449-517.
[Wor1984]Worley, Dale Raymond, A theory of shifted Young tableaux. Dissertation, Massachusetts Institute of Technology, 1984.
[WP-Bessel]Wikipedia article Bessel_function
[WP-Error]Wikipedia article Error_function
[WP-Struve]Wikipedia article Struve_function
[WSK1997]D. Wagner, B. Schneier, and J. Kelsey, Cryptoanalysis of the cellular encryption algorithm; in CRYPTO, (1997), pp. 526-537.
[Wu2009]Hongjun Wu, The Hash Function JH; submitted to NIST, (2008), available at
[WW2005]Ralf-Philipp Weinmann and Kai Wirt, Analysis of the DVB Common Scrambling Algorithm; in IFIP TC-6 TC-11, (2005).
[WZY2015]WenLing Wu, Lei Zhang, and XiaoLi Yu, The DBlock family of block ciphers; in Science China Information Sciences, (2015), pp. 1-14.


[XP1994]Deng Xiaotie, and Christos Papadimitriou. On the complexity of cooperative solution concepts. Mathematics of Operations Research 19.2 (1994): 257-266.


[Yamada2007]Daisuke Yamada. Scattering rule in soliton cellular automaton associated with crystal base of \(U_q(D_4^{(3)})\). J. Math. Phys., 48 (4):043509, 28, (2007).
[Yoc2005]Jean-Christophe Yoccoz “Echange d’Intervalles”, Cours au college de France
[Yun1976]Yun, David YY. On square-free decomposition algorithms. In Proceedings of the third ACM symposium on Symbolic and algebraic computation, pp. 26-35. ACM, 1976.
[Yuz1993]Sergey Yuzvinsky, “The first two obstructions to the freeness of arrangements”, Transactions of the American Mathematical Society, Vol. 335, 1 (1993) pp. 231–244.
[YWHWXSW2014]D. Ye, P. Wang, L. Hu, L. Wang, Y. Xie, S. Sun, and P. Wang, Panda v1; in CAESAR Competition, (2014).


[ZBLRYV2015]W. Zhang, Z. Bao, D. Lin, V. Rijmen, B. Yang, and I. Verbauwhede, RECTANGLE: A bit-slice lightweight block cipher suitable for multiple platforms; in SCience China Information Sciences, (2015), pp. 1-15.
[ZBN1997]C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization. ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp.550–560, 1997.
[Zie1998]G. M. Ziegler. Shelling polyhedral 3-balls and 4-polytopes. Discrete Comput. Geom. 19 (1998), 159-174.
[Zie2007]G. M. Ziegler. Lectures on polytopes, Volume 152 of Graduate Texts in Mathematics, 7th printing of 1st edition, Springer, 2007.
[Zor2008]A. Zorich “Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials”, Journal of Modern Dynamics, vol. 2, no 1, 139-185 (2008) (
[Zor]Anton Zorich, “Generalized Permutation software” (
[ZZ2005]Hechun Zhang and R. B. Zhang. Dual canonical bases for the quantum special linear group and invariant subalgebras. Lett. Math. Phys. 73 (2005), pp. 165-181. Arxiv math/0509651.

Indices and Tables