Identifier
- St000235: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 2
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 0
[3,1,2] => 3
[3,2,1] => 2
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 2
[1,4,2,3] => 4
[1,4,3,2] => 4
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 4
[3,1,4,2] => 3
[3,2,1,4] => 4
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 4
[4,1,3,2] => 4
[4,2,1,3] => 4
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 2
[1,2,3,4,5] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 3
[1,2,5,3,4] => 5
[1,2,5,4,3] => 5
[1,3,2,4,5] => 4
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 2
[1,3,5,2,4] => 4
[1,3,5,4,2] => 4
[1,4,2,3,5] => 5
[1,4,2,5,3] => 4
[1,4,3,2,5] => 5
[1,4,3,5,2] => 4
[1,4,5,2,3] => 5
[1,4,5,3,2] => 5
[1,5,2,3,4] => 5
[1,5,2,4,3] => 5
[1,5,3,2,4] => 5
[1,5,3,4,2] => 5
[1,5,4,2,3] => 4
[1,5,4,3,2] => 4
[2,1,3,4,5] => 4
[2,1,3,5,4] => 3
[2,1,4,3,5] => 3
[2,1,4,5,3] => 2
[2,1,5,3,4] => 4
[2,1,5,4,3] => 4
[2,3,1,4,5] => 3
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 0
[2,3,5,1,4] => 3
[2,3,5,4,1] => 2
[2,4,1,3,5] => 4
[2,4,1,5,3] => 3
[2,4,3,1,5] => 4
[2,4,3,5,1] => 2
[2,4,5,1,3] => 4
[2,4,5,3,1] => 3
[2,5,1,3,4] => 4
[2,5,1,4,3] => 4
[2,5,3,1,4] => 4
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 2
[3,1,2,4,5] => 5
[3,1,2,5,4] => 4
[3,1,4,2,5] => 4
[3,1,4,5,2] => 3
[3,1,5,2,4] => 5
[3,1,5,4,2] => 5
[3,2,1,4,5] => 5
[3,2,1,5,4] => 4
[3,2,4,1,5] => 4
[3,2,4,5,1] => 2
[3,2,5,1,4] => 5
[3,2,5,4,1] => 4
[3,4,1,2,5] => 5
[3,4,1,5,2] => 4
[3,4,2,1,5] => 5
[3,4,2,5,1] => 3
[3,4,5,1,2] => 5
[3,4,5,2,1] => 4
[3,5,1,2,4] => 5
[3,5,1,4,2] => 5
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Description
The number of indices that are not cyclical small weak excedances.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
References
[1] Li, Y. Ménage Numbers and Ménage Permutations arXiv:1502.06068
Code
def statistic(pi):
n = len(pi)
return sum(1 for i in range(n) if pi[i] != ((i+1) % n) + 1)
Created
Feb 24, 2015 at 13:16 by Christian Stump
Updated
Sep 08, 2023 at 11:45 by Martin Rubey
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