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()                                                # needs sage.groups
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))                                    # needs sage.groups
sage: a.transport(p)                                                        # needs sage.groups
['b', 'a', 'c']

sage.combinat.species.linear_order_species.LinearOrderSpecies_class#: alias of LinearOrderSpecies