Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001862
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Mapping
St001862: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[-1] => 0
[1,2] => 0
[1,-2] => 0
[-1,2] => 0
[-1,-2] => 0
[2,1] => 0
[2,-1] => 1
[-2,1] => 0
[-2,-1] => 1
[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] => 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
[2,1,3] => 0
[2,1,-3] => 0
[2,-1,3] => 1
[2,-1,-3] => 1
[-2,1,3] => 0
[-2,1,-3] => 0
[-2,-1,3] => 1
[-2,-1,-3] => 1
[2,3,1] => 1
[2,3,-1] => 2
[2,-3,1] => 1
[2,-3,-1] => 2
[-2,3,1] => 1
[-2,3,-1] => 2
[-2,-3,1] => 1
[-2,-3,-1] => 2
[3,1,2] => 0
[3,1,-2] => 1
[3,-1,2] => 1
[3,-1,-2] => 2
[-3,1,2] => 0
[-3,1,-2] => 1
[-3,-1,2] => 1
[-3,-1,-2] => 2
Description
The number of crossings of a signed permutation. A crossing of a signed permutation $\pi$ is a pair $(i, j)$ of indices such that * $i < j \leq \pi(i) < \pi(j)$, or * $-i < j \leq -\pi(i) < \pi(j)$, or * $i > j > \pi(i) > \pi(j)$.