Linear-order Species

sage.combinat.species.linear_order_species.LinearOrderSpecies(*args, **kwds)

Returns the species of linear orders.

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: L.generating_series().coefficients(5)
[1, 1, 1, 1, 1]
class sage.combinat.species.linear_order_species.LinearOrderSpeciesStructure(parent, labels, list)
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']
class sage.combinat.species.linear_order_species.LinearOrderSpecies_class(min=None, max=None, weight=None)
__init__(min=None, max=None, weight=None)

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: L._check()
True
sage: L == loads(dumps(L))
True
static _cached_constructor(*args, **kwds)

Returns the species of linear orders.

EXAMPLES:

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

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: g = L.cycle_index_series()
sage: g.coefficients(5)
[p[], p[1], p[1, 1], p[1, 1, 1], p[1, 1, 1, 1]]
_default_structure_class
alias of LinearOrderSpeciesStructure
_gs_list(base_ring)

The generating series for the species of linear orders is \frac{1}{1-x}.

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: g = L.generating_series()
sage: g.coefficients(10)
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
_isotypes(structure_class, labels)

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: L.isotypes([1,2,3]).list()
[[1, 2, 3]]
_itgs_list(base_ring)

The isomorphism type generating series is given by \frac{1}{1-x}.

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: g = L.isotype_generating_series()
sage: g.coefficients(10)
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
_structures(structure_class, labels)

EXAMPLES:

sage: L = species.LinearOrderSpecies()
sage: L.structures([1,2,3]).list()
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]

Previous topic

Permutation species

Next topic

Set Species

This Page