Identifier
- St001375: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 1
[2,1,4,3] => 3
[2,3,1,4] => 2
[2,3,4,1] => 2
[2,4,1,3] => 4
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 4
[3,2,1,4] => 1
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 2
[4,1,2,3] => 2
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 0
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 3
[1,3,2,4,5] => 3
[1,3,2,5,4] => 5
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 5
[1,3,5,4,2] => 4
[1,4,2,3,5] => 3
[1,4,2,5,3] => 5
[1,4,3,2,5] => 3
[1,4,3,5,2] => 5
[1,4,5,2,3] => 3
[1,4,5,3,2] => 4
[1,5,2,3,4] => 3
[1,5,2,4,3] => 4
[1,5,3,2,4] => 5
[1,5,3,4,2] => 5
[1,5,4,2,3] => 4
[1,5,4,3,2] => 3
[2,1,3,4,5] => 1
[2,1,3,5,4] => 4
[2,1,4,3,5] => 3
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 4
[2,3,1,4,5] => 2
[2,3,1,5,4] => 4
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 4
[2,3,5,4,1] => 3
[2,4,1,3,5] => 4
[2,4,1,5,3] => 5
[2,4,3,1,5] => 3
[2,4,3,5,1] => 5
[2,4,5,1,3] => 4
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 5
[2,5,3,1,4] => 5
[2,5,3,4,1] => 4
[2,5,4,1,3] => 4
[2,5,4,3,1] => 3
[3,1,2,4,5] => 2
[3,1,2,5,4] => 4
[3,1,4,2,5] => 4
[3,1,4,5,2] => 4
[3,1,5,2,4] => 5
[3,1,5,4,2] => 5
[3,2,1,4,5] => 1
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 3
[3,4,1,5,2] => 4
[3,4,2,1,5] => 2
[3,4,2,5,1] => 4
[3,4,5,1,2] => 3
[3,4,5,2,1] => 2
[3,5,1,2,4] => 4
[3,5,1,4,2] => 5
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Description
The pancake length of a permutation.
This is the minimal number of pancake moves needed to generate a permutation where a pancake move is a reversal of a prefix in a permutation.
This is the minimal number of pancake moves needed to generate a permutation where a pancake move is a reversal of a prefix in a permutation.
References
[1] Blanco, S. A., Buehrle, C. Some relations on prefix reversal generators of the symmetric and hyperoctahedral group arXiv:1803.01760
Code
@cached_function
def generate_group_from_generators(parent, gens):
gens = list(gens)
inds = range(len(gens))
assert all( gen.parent() == parent for gen in gens )
one = parent.one()
level_set_cur = set([one])
found_elements = set([one])
level_sets = []
while level_set_cur:
level_sets.append(level_set_cur)
level_set_new = set()
for x in level_set_cur:
for i in inds:
y = x * gens[i]
if y not in found_elements:
found_elements.add(y)
level_set_new.add(y)
level_set_cur = level_set_new
return level_sets
@cached_function
def pancake_gens(n):
return tuple(Permutations(n)(list(range(k,0,-1))+list(range(k+1,n+1))) for k in [2 .. n])
def statistic(sigma):
n = len(sigma)
level_sets = generate_group_from_generators(Permutations(n), pancake_gens(n))
i = 0
for level in level_sets:
if sigma not in level:
i += 1
else:
return i
Created
Mar 25, 2019 at 14:37 by Christian Stump
Updated
Mar 09, 2023 at 13:53 by Tilman Möller
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