Identifier
Values
[1] => 0
[-1] => 0
[1,2] => 0
[1,-2] => 0
[-1,2] => 0
[-1,-2] => 0
[2,1] => 0
[2,-1] => 0
[-2,1] => 0
[-2,-1] => 0
[1,2,3] => 0
[1,2,-3] => 0
[1,-2,3] => 0
[1,-2,-3] => 0
[-1,2,3] => 0
[-1,2,-3] => 0
[-1,-2,3] => 0
[-1,-2,-3] => 0
[1,3,2] => 1
[1,3,-2] => 0
[1,-3,2] => 1
[1,-3,-2] => 0
[-1,3,2] => 1
[-1,3,-2] => 0
[-1,-3,2] => 1
[-1,-3,-2] => 0
[2,1,3] => 0
[2,1,-3] => 0
[2,-1,3] => 0
[2,-1,-3] => 0
[-2,1,3] => 0
[-2,1,-3] => 0
[-2,-1,3] => 0
[-2,-1,-3] => 0
[2,3,1] => 0
[2,3,-1] => 0
[2,-3,1] => 0
[2,-3,-1] => 0
[-2,3,1] => 0
[-2,3,-1] => 0
[-2,-3,1] => 0
[-2,-3,-1] => 0
[3,1,2] => 0
[3,1,-2] => 0
[3,-1,2] => 1
[3,-1,-2] => 0
[-3,1,2] => 0
[-3,1,-2] => 0
[-3,-1,2] => 1
[-3,-1,-2] => 0
[3,2,1] => 0
[3,2,-1] => 0
[3,-2,1] => 0
[3,-2,-1] => 0
[-3,2,1] => 0
[-3,2,-1] => 0
[-3,-2,1] => 0
[-3,-2,-1] => 0
[1,2,3,4] => 0
[1,2,3,-4] => 0
[1,2,-3,4] => 0
[1,2,-3,-4] => 0
[1,-2,3,4] => 0
[1,-2,3,-4] => 0
[1,-2,-3,4] => 0
[1,-2,-3,-4] => 0
[-1,2,3,4] => 0
[-1,2,3,-4] => 0
[-1,2,-3,4] => 0
[-1,2,-3,-4] => 0
[-1,-2,3,4] => 0
[-1,-2,3,-4] => 0
[-1,-2,-3,4] => 0
[-1,-2,-3,-4] => 0
[1,2,4,3] => 2
[1,2,4,-3] => 0
[1,2,-4,3] => 2
[1,2,-4,-3] => 0
[1,-2,4,3] => 2
[1,-2,4,-3] => 0
[1,-2,-4,3] => 2
[1,-2,-4,-3] => 0
[-1,2,4,3] => 2
[-1,2,4,-3] => 0
[-1,2,-4,3] => 2
[-1,2,-4,-3] => 0
[-1,-2,4,3] => 2
[-1,-2,4,-3] => 0
[-1,-2,-4,3] => 2
[-1,-2,-4,-3] => 0
[1,3,2,4] => 1
[1,3,2,-4] => 1
[1,3,-2,4] => 0
[1,3,-2,-4] => 0
[1,-3,2,4] => 1
[1,-3,2,-4] => 1
[1,-3,-2,4] => 0
[1,-3,-2,-4] => 0
[-1,3,2,4] => 1
[-1,3,2,-4] => 1
[-1,3,-2,4] => 0
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Description
The number of alignments of type EN of a signed permutation.
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
- $-i < 0 < -\pi(i) < \pi(j) < j$
- $i \leq\pi(i) < \pi(j) < j$.
References
[1] Cho, S., Park, K. Permutation statistics and weak \B\ruhat order in permutation tableaux of type $B$ arXiv:1412.6290
Code
def statistic(pi):
n = len(pi)
A_EN = [(i, j) for i in range(1, n+1) for j in range(1, n+1)
if (-i < 0 < -pi(i) < pi(j) < j)
or (i <= pi(i) < pi(j) < j)]
return len(A_EN)
Created
Dec 01, 2022 at 11:41 by Martin Rubey
Updated
Dec 01, 2022 at 11:41 by Martin Rubey
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