# Linear-order Species¶

class sage.combinat.species.linear_order_species.LinearOrderSpecies(min=None, max=None, weight=None)

Returns the species of linear orders.

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: L.generating_series().coefficients(5)
[1, 1, 1, 1, 1]

sage: L = species.LinearOrderSpecies()
sage: L._check()
True
True

class sage.combinat.species.linear_order_species.LinearOrderSpeciesStructure(parent, labels, list)

This is a base class from which the classes for the structures inherit.

EXAMPLES:

sage: from sage.combinat.species.structure import GenericSpeciesStructure
sage: a = GenericSpeciesStructure(None, [2,3,4], [1,2,3])
sage: a
[2, 3, 4]
sage: a.parent() is None
True
True

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"]).random_element(); 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"]).random_element(); 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