Linear-order Species#
- class sage.combinat.species.linear_order_species.LinearOrderSpecies(min=None, max=None, weight=None)#
Bases:
GenericCombinatorialSpecies
,UniqueRepresentation
Returns the species of linear orders.
EXAMPLES:
sage: L = species.LinearOrderSpecies() sage: L.generating_series()[0:5] [1, 1, 1, 1, 1] sage: L = species.LinearOrderSpecies() sage: L._check() True sage: L == loads(dumps(L)) True
- class sage.combinat.species.linear_order_species.LinearOrderSpeciesStructure(parent, labels, list)#
Bases:
GenericSpeciesStructure
- automorphism_group()#
Returns the group of permutations whose action on this structure leave it fixed. For the species of linear orders, there is no non-trivial automorphism.
EXAMPLES:
sage: F = species.LinearOrderSpecies() sage: a = F.structures(["a", "b", "c"])[0]; a ['a', 'b', 'c'] sage: a.automorphism_group() Symmetric group of order 1! as a permutation group
- canonical_label()#
EXAMPLES:
sage: P = species.LinearOrderSpecies() sage: s = P.structures(["a", "b", "c"]).random_element() sage: s.canonical_label() ['a', 'b', 'c']
- transport(perm)#
Returns the transport of this structure along the permutation perm.
EXAMPLES:
sage: F = species.LinearOrderSpecies() sage: a = F.structures(["a", "b", "c"])[0]; a ['a', 'b', 'c'] sage: p = PermutationGroupElement((1,2)) sage: a.transport(p) ['b', 'a', 'c']
- sage.combinat.species.linear_order_species.LinearOrderSpecies_class#
alias of
LinearOrderSpecies