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# Linear-order Species

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

  Bases: `sage.combinat.species.species.GenericCombinatorialSpecies`, `sage.structure.unique_representation.UniqueRepresentation`

  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
      sage: L == loads(dumps(L))
      True

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

  Bases: `sage.combinat.species.structure.GenericSpeciesStructure`

  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
      sage: a == loads(dumps(a))
      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`

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