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Matching statistic: St001907
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Mapping
St001907: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[-1] => 1
[1,2] => 0
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 1
[2,1] => 1
[2,-1] => 2
[-2,1] => 1
[-2,-1] => 1
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 1
[-1,2,3] => 1
[-1,2,-3] => 1
[-1,-2,3] => 1
[-1,-2,-3] => 2
[1,3,2] => 1
[1,3,-2] => 2
[1,-3,2] => 1
[1,-3,-2] => 1
[-1,3,2] => 2
[-1,3,-2] => 2
[-1,-3,2] => 1
[-1,-3,-2] => 2
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 2
[2,-1,-3] => 2
[-2,1,3] => 1
[-2,1,-3] => 1
[-2,-1,3] => 1
[-2,-1,-3] => 2
[2,3,1] => 2
[2,3,-1] => 3
[2,-3,1] => 2
[2,-3,-1] => 2
[-2,3,1] => 2
[-2,3,-1] => 2
[-2,-3,1] => 1
[-2,-3,-1] => 2
[3,1,2] => 1
[3,1,-2] => 2
[3,-1,2] => 2
[3,-1,-2] => 2
[-3,1,2] => 1
[-3,1,-2] => 1
[-3,-1,2] => 1
[-3,-1,-2] => 2
Description
The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. For a signed permutation $\sigma$, this equals $$ \left\lfloor \dfrac{fexc(\sigma)+1}{2} \right\rfloor = exc(\sigma) + \left\lfloor \dfrac{neg(\sigma)+1}{2} \right\rfloor, $$ where $$fexc(\sigma) = 2exc(\sigma) + neg(\sigma),$$ $$exc(\sigma) = |\{i \in [n-1] \,:\, \sigma(i) > i\}|,$$ $$neg(\sigma) = |\{i \in [n] \,:\, \sigma(i) < 0\}|.$$ This statistic has the same distribution as the descent statistic [[St001427]].