def cyclic_permutations_of_set_partition_iterator(set_part):
"""
Iterates over all combinations of cyclic permutations of each cell
of the set partition.
AUTHORS:
- Robert L. Miller
EXAMPLES::
sage: from sage.combinat.set_partition import cyclic_permutations_of_set_partition_iterator
sage: list(cyclic_permutations_of_set_partition_iterator([[1,2,3,4],[5,6,7]]))
[[[1, 2, 3, 4], [5, 6, 7]],
[[1, 2, 4, 3], [5, 6, 7]],
[[1, 3, 2, 4], [5, 6, 7]],
[[1, 3, 4, 2], [5, 6, 7]],
[[1, 4, 2, 3], [5, 6, 7]],
[[1, 4, 3, 2], [5, 6, 7]],
[[1, 2, 3, 4], [5, 7, 6]],
[[1, 2, 4, 3], [5, 7, 6]],
[[1, 3, 2, 4], [5, 7, 6]],
[[1, 3, 4, 2], [5, 7, 6]],
[[1, 4, 2, 3], [5, 7, 6]],
[[1, 4, 3, 2], [5, 7, 6]]]
"""
from sage.combinat.permutation import CyclicPermutations
if len(set_part) == 1:
for i in CyclicPermutations(set_part[0]):
yield [i]
else:
for right in cyclic_permutations_of_set_partition_iterator(
set_part[1:]):
for perm in CyclicPermutations(set_part[0]):
yield [perm] + right
def _structures(self, structure_class, labels):
"""
EXAMPLES::
sage: P = species.CycleSpecies()
sage: P.structures([1,2,3]).list()
[(1, 2, 3), (1, 3, 2)]
"""
from sage.combinat.permutation import CyclicPermutations
for c in CyclicPermutations(range(1, len(labels) + 1)):
yield structure_class(self, labels, c)