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Matching statistic: St001823
Mapping
St001823: 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] => 2
[-1,2] => 1
[-1,-2] => 3
[2,1] => 1
[2,-1] => 1
[-2,1] => 2
[-2,-1] => 2
[1,2,3] => 0
[1,2,-3] => 3
[1,-2,3] => 2
[1,-2,-3] => 5
[-1,2,3] => 1
[-1,2,-3] => 4
[-1,-2,3] => 3
[-1,-2,-3] => 6
[1,3,2] => 1
[1,3,-2] => 2
[1,-3,2] => 3
[1,-3,-2] => 4
[-1,3,2] => 2
[-1,3,-2] => 3
[-1,-3,2] => 4
[-1,-3,-2] => 5
[2,1,3] => 1
[2,1,-3] => 4
[2,-1,3] => 1
[2,-1,-3] => 4
[-2,1,3] => 2
[-2,1,-3] => 5
[-2,-1,3] => 2
[-2,-1,-3] => 5
[2,3,1] => 1
[2,3,-1] => 2
[2,-3,1] => 3
[2,-3,-1] => 4
[-2,3,1] => 2
[-2,3,-1] => 3
[-2,-3,1] => 4
[-2,-3,-1] => 5
[3,1,2] => 1
[3,1,-2] => 4
[3,-1,2] => 1
[3,-1,-2] => 4
[-3,1,2] => 2
[-3,1,-2] => 5
[-3,-1,2] => 2
[-3,-1,-2] => 5
Description
The Stasinski-Voll length of a signed permutation. The Stasinski-Voll length of a signed permutation $\sigma$ is $$ L(\sigma) = \frac{1}{2} \#\{(i,j) ~\mid -n \leq i < j \leq n,~ i \not\equiv j \operatorname{mod} 2,~ \sigma(i) > \sigma(j)\}, $$ where $n$ is the size of $\sigma$.