Identifier
Values
[1] => 0
[-1] => 0
[1,2] => 0
[1,-2] => 0
[-1,2] => 0
[-1,-2] => 0
[2,1] => 1
[2,-1] => 1
[-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] => 1
[1,-3,2] => 0
[1,-3,-2] => 0
[-1,3,2] => 1
[-1,3,-2] => 1
[-1,-3,2] => 0
[-1,-3,-2] => 0
[2,1,3] => 1
[2,1,-3] => 1
[2,-1,3] => 1
[2,-1,-3] => 1
[-2,1,3] => 0
[-2,1,-3] => 0
[-2,-1,3] => 0
[-2,-1,-3] => 0
[2,3,1] => 2
[2,3,-1] => 2
[2,-3,1] => 1
[2,-3,-1] => 1
[-2,3,1] => 1
[-2,3,-1] => 1
[-2,-3,1] => 0
[-2,-3,-1] => 0
[3,1,2] => 1
[3,1,-2] => 1
[3,-1,2] => 1
[3,-1,-2] => 1
[-3,1,2] => 0
[-3,1,-2] => 0
[-3,-1,2] => 0
[-3,-1,-2] => 0
[3,2,1] => 1
[3,2,-1] => 1
[3,-2,1] => 1
[3,-2,-1] => 1
[-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] => 1
[1,2,4,-3] => 1
[1,2,-4,3] => 0
[1,2,-4,-3] => 0
[1,-2,4,3] => 1
[1,-2,4,-3] => 1
[1,-2,-4,3] => 0
[1,-2,-4,-3] => 0
[-1,2,4,3] => 1
[-1,2,4,-3] => 1
[-1,2,-4,3] => 0
[-1,2,-4,-3] => 0
[-1,-2,4,3] => 1
[-1,-2,4,-3] => 1
[-1,-2,-4,3] => 0
[-1,-2,-4,-3] => 0
[1,3,2,4] => 1
[1,3,2,-4] => 1
[1,3,-2,4] => 1
[1,3,-2,-4] => 1
[1,-3,2,4] => 0
[1,-3,2,-4] => 0
[1,-3,-2,4] => 0
[1,-3,-2,-4] => 0
[-1,3,2,4] => 1
[-1,3,2,-4] => 1
[-1,3,-2,4] => 1
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Description
The number of excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) > i\}\rvert$.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) > i\}\rvert$.
References
[1] Corteel, S., Josuat-Vergès, M., Kim, J. S. Crossings of signed permutations and $q$-Eulerian numbers of type $B$ MathSciNet:3096133
Code
def statistic(pi):
return sum(1 for i in range(len(pi)) if pi[i] > i + 1)
Created
Nov 30, 2022 at 23:53 by Martin Rubey
Updated
Nov 30, 2022 at 23:53 by Martin Rubey
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