Identifier
- St000279: Permutations ⟶ ℤ
Values
[1,2] => 2
[2,1] => 0
[1,2,3] => 4
[1,3,2] => 2
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 8
[1,2,4,3] => 4
[1,3,2,4] => 4
[1,3,4,2] => 2
[1,4,2,3] => 4
[1,4,3,2] => 2
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 0
[3,1,2,4] => 0
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 16
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 4
[1,2,5,3,4] => 8
[1,2,5,4,3] => 4
[1,3,2,4,5] => 8
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 4
[1,3,5,4,2] => 2
[1,4,2,3,5] => 8
[1,4,2,5,3] => 4
[1,4,3,2,5] => 4
[1,4,3,5,2] => 2
[1,4,5,2,3] => 4
[1,4,5,3,2] => 2
[1,5,2,3,4] => 8
[1,5,2,4,3] => 4
[1,5,3,2,4] => 4
[1,5,3,4,2] => 2
[1,5,4,2,3] => 4
[1,5,4,3,2] => 2
[2,1,3,4,5] => 0
[2,1,3,5,4] => 0
[2,1,4,3,5] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,4,3] => 0
[2,3,1,4,5] => 0
[2,3,1,5,4] => 0
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,4,1] => 0
[2,4,1,3,5] => 0
[2,4,1,5,3] => 0
[2,4,3,1,5] => 0
[2,4,3,5,1] => 0
[2,4,5,1,3] => 0
[2,4,5,3,1] => 0
[2,5,1,3,4] => 0
[2,5,1,4,3] => 0
[2,5,3,1,4] => 0
[2,5,3,4,1] => 0
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,4,5] => 0
[3,1,2,5,4] => 0
[3,1,4,2,5] => 0
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,4,2] => 0
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 0
[3,2,4,5,1] => 0
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 0
[3,4,2,1,5] => 0
[3,4,2,5,1] => 0
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 0
[3,5,1,4,2] => 0
[3,5,2,1,4] => 0
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Description
The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations.
Code
def cycle_to_one_line(pi):
return Permutation(sum([list(t) for t in pi.cycle_tuples()],[]))
@cached_function
def preimages(level):
result = dict()
for el in Permutations(level):
image = cycle_to_one_line(el)
result[image] = result.get(image, 0) + 1
return result
def statistic(x):
return preimages(x.size()).get(x, 0)
Created
Sep 11, 2015 at 22:54 by Martin Rubey
Updated
Jan 07, 2021 at 15:42 by Martin Rubey
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