Identifier
Values
[1] => 2
[-1] => 1
[1,2] => 4
[1,-2] => 3
[-1,2] => 3
[-1,-2] => 2
[2,1] => 2
[2,-1] => 3
[-2,1] => 1
[-2,-1] => 2
[1,2,3] => 6
[1,2,-3] => 5
[1,-2,3] => 5
[1,-2,-3] => 4
[-1,2,3] => 5
[-1,2,-3] => 4
[-1,-2,3] => 4
[-1,-2,-3] => 3
[1,3,2] => 4
[1,3,-2] => 5
[1,-3,2] => 3
[1,-3,-2] => 4
[-1,3,2] => 3
[-1,3,-2] => 4
[-1,-3,2] => 2
[-1,-3,-2] => 3
[2,1,3] => 4
[2,1,-3] => 3
[2,-1,3] => 5
[2,-1,-3] => 4
[-2,1,3] => 3
[-2,1,-3] => 2
[-2,-1,3] => 4
[-2,-1,-3] => 3
[2,3,1] => 4
[2,3,-1] => 5
[2,-3,1] => 3
[2,-3,-1] => 4
[-2,3,1] => 3
[-2,3,-1] => 4
[-2,-3,1] => 2
[-2,-3,-1] => 3
[3,1,2] => 2
[3,1,-2] => 3
[3,-1,2] => 3
[3,-1,-2] => 4
[-3,1,2] => 1
[-3,1,-2] => 2
[-3,-1,2] => 2
[-3,-1,-2] => 3
[3,2,1] => 4
[3,2,-1] => 5
[3,-2,1] => 3
[3,-2,-1] => 4
[-3,2,1] => 3
[-3,2,-1] => 4
[-3,-2,1] => 2
[-3,-2,-1] => 3
[1,2,3,4] => 8
[1,2,3,-4] => 7
[1,2,-3,4] => 7
[1,2,-3,-4] => 6
[1,-2,3,4] => 7
[1,-2,3,-4] => 6
[1,-2,-3,4] => 6
[1,-2,-3,-4] => 5
[-1,2,3,4] => 7
[-1,2,3,-4] => 6
[-1,2,-3,4] => 6
[-1,2,-3,-4] => 5
[-1,-2,3,4] => 6
[-1,-2,3,-4] => 5
[-1,-2,-3,4] => 5
[-1,-2,-3,-4] => 4
[1,2,4,3] => 6
[1,2,4,-3] => 7
[1,2,-4,3] => 5
[1,2,-4,-3] => 6
[1,-2,4,3] => 5
[1,-2,4,-3] => 6
[1,-2,-4,3] => 4
[1,-2,-4,-3] => 5
[-1,2,4,3] => 5
[-1,2,4,-3] => 6
[-1,2,-4,3] => 4
[-1,2,-4,-3] => 5
[-1,-2,4,3] => 4
[-1,-2,4,-3] => 5
[-1,-2,-4,3] => 3
[-1,-2,-4,-3] => 4
[1,3,2,4] => 6
[1,3,2,-4] => 5
[1,3,-2,4] => 7
[1,3,-2,-4] => 6
[1,-3,2,4] => 5
[1,-3,2,-4] => 4
[1,-3,-2,4] => 6
[1,-3,-2,-4] => 5
[-1,3,2,4] => 5
[-1,3,2,-4] => 4
[-1,3,-2,4] => 6
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Description
The number of flag weak exceedances of a signed permutation.
This is the number of negative entries plus twice the number of weak exceedances of the signed permutation.
This is the number of negative entries plus twice the number of weak exceedances of the signed permutation.
References
[1] Eu, S.-P., Fu, T.-S., Hsu, H.-C., Liao, H.-C. Signed Countings of types B and D permutations and $t,q$-Euler Numbers arXiv:1708.05518
Code
def statistic(pi):
neg = sum(1 for a in pi if a < 0)
wex = sum(1 for i, a in enumerate(pi, 1) if a >= i)
return 2*wex + neg
Created
Jul 20, 2022 at 05:57 by Martin Rubey
Updated
Jul 20, 2022 at 05:57 by Martin Rubey
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