Enumerated sets and combinatorial objects

Todo

Proofread / point to the main classes rather than the modules

Categories

• EnumeratedSets, FiniteEnumeratedSets

Basic enumerated sets

• Subsets, Combinations

• Arrangements, Tuples

• FiniteEnumeratedSet

• DisjointUnionEnumeratedSets

Integer lists

• Integer partitions (see also: Enumerated sets of partitions, tableaux, …)

• Integer compositions

• SignedCompositions

• IntegerListsLex

• Super Partitions

• IntegerVectors

• WeightedIntegerVectors()

• IntegerVectorsModPermutationGroup

• Parking Functions

• Non-Decreasing Parking Functions

• Sidon sets and their generalizations, Sidon g-sets

Words

• Words

• Subwords

• Necklaces

• Lyndon words

• Dyck Words

• De Bruijn sequences

• Shuffle product of iterables

Permutations, …

• Permutations

• Permutations (Cython file)

• Affine Permutations

• Arrangements

• Derangements

• Baxter permutations

See also

• SymmetricGroup, PermutationGroup(), Catalog of permutation groups

• FiniteSetMaps

• Integer vectors modulo the action of a permutation group

• Robinson-Schensted-Knuth correspondence

Partitions, tableaux, …

See: Enumerated sets of partitions, tableaux, …

Polyominoes

See: Parallelogram Polyominoes

Integer matrices, …

• Counting, generating, and manipulating non-negative integer matrices

• Hadamard matrices

• Latin Squares

• Alternating Sign Matrices

• Six Vertex Model

• Similarity class types of matrices with entries in a finite field

• Restricted growth arrays

• Vector Partitions

See also

• MatrixSpace

• Library of Interesting Groups

Subsets and set partitions

• Subsets, Combinations

• PairwiseCompatibleSubsets

• Subsets satisfying a hereditary property

• Ordered Set Partitions

• Set Partitions

• Diagram and Partition Algebras

• OrderedMultisetPartitionsIntoSets, OrderedMultisetPartitionIntoSets

Trees

• Abstract Recursive Trees

• Ordered Rooted Trees

• Binary Trees

• Rooted (Unordered) Trees

Enumerated sets related to graphs

• Degree sequences

• Paths in Directed Acyclic Graphs

• Perfect matchings

Backtracking solvers and generic enumerated sets

Todo

Do we want a separate section, possibly more proeminent, for backtracking solvers?

• RecursivelyEnumeratedSet()

• GenericBacktracker

• sage.parallel.map_reduce

• Tiling Solver

• Exact Cover Problem via Dancing Links

• Dancing links C++ wrapper

• Combinatorial species

• IntegerListsLex

• IntegerVectorsModPermutationGroup

Low level enumerated sets

• Gray codes

Misc enumerated sets

• GelfandTsetlinPattern, GelfandTsetlinPatterns

• KnutsonTaoPuzzleSolver

• LatticePolytope()