Permutation species#
- class sage.combinat.species.permutation_species.PermutationSpecies(min=None, max=None, weight=None)#
Bases:
GenericCombinatorialSpecies
,UniqueRepresentation
Returns the species of permutations.
EXAMPLES:
sage: P = species.PermutationSpecies() sage: P.generating_series()[0:5] [1, 1, 1, 1, 1] sage: P.isotype_generating_series()[0:5] [1, 1, 2, 3, 5] sage: P = species.PermutationSpecies() sage: c = P.generating_series()[0:3] sage: P._check() True sage: P == loads(dumps(P)) True
- class sage.combinat.species.permutation_species.PermutationSpeciesStructure(parent, labels, list)#
Bases:
GenericSpeciesStructure
- automorphism_group()#
Returns the group of permutations whose action on this structure leave it fixed.
EXAMPLES:
sage: set_random_seed(0) sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.automorphism_group() Permutation Group with generators [(2,3), (1,4)]
sage: [a.transport(perm) for perm in a.automorphism_group()] [['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd']]
- canonical_label()#
EXAMPLES:
sage: P = species.PermutationSpecies() sage: S = P.structures(["a", "b", "c"]) sage: [s.canonical_label() for s in S] [['a', 'b', 'c'], ['b', 'a', 'c'], ['b', 'a', 'c'], ['b', 'c', 'a'], ['b', 'c', 'a'], ['b', 'a', 'c']]
- permutation_group_element()#
Returns self as a permutation group element.
EXAMPLES:
sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.permutation_group_element() (2,3)
- transport(perm)#
Returns the transport of this structure along the permutation perm.
EXAMPLES:
sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.transport(p) ['a', 'd', 'c', 'b']
- sage.combinat.species.permutation_species.PermutationSpecies_class#
alias of
PermutationSpecies