Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001822
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Mapping
St001822: 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] => 1
[-1,2] => 1
[-1,-2] => 1
[2,1] => 0
[2,-1] => 0
[-2,1] => 0
[-2,-1] => 0
[1,2,3] => 0
[1,2,-3] => 2
[1,-2,3] => 2
[1,-2,-3] => 3
[-1,2,3] => 2
[-1,2,-3] => 3
[-1,-2,3] => 3
[-1,-2,-3] => 3
[1,3,2] => 1
[1,3,-2] => 1
[1,-3,2] => 2
[1,-3,-2] => 2
[-1,3,2] => 2
[-1,3,-2] => 2
[-1,-3,2] => 2
[-1,-3,-2] => 2
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 1
[2,-1,-3] => 2
[-2,1,3] => 2
[-2,1,-3] => 2
[-2,-1,3] => 2
[-2,-1,-3] => 2
[2,3,1] => 0
[2,3,-1] => 0
[2,-3,1] => 1
[2,-3,-1] => 1
[-2,3,1] => 1
[-2,3,-1] => 1
[-2,-3,1] => 1
[-2,-3,-1] => 1
[3,1,2] => 0
[3,1,-2] => 1
[3,-1,2] => 1
[3,-1,-2] => 1
[-3,1,2] => 0
[-3,1,-2] => 1
[-3,-1,2] => 1
[-3,-1,-2] => 1
Description
The number of alignments of a signed permutation. An alignment of a signed permutation $n\in\mathfrak H_n$ is either a nesting alignment, [[St001866]], an alignment of type EN, [[St001867]], or an alignment of type NE, [[St001868]]. Let $\operatorname{al}$ be the number of alignments of $\pi$, let \operatorname{cr} be the number of crossings, [[St001862]], let \operatorname{wex} be the number of weak excedances, [[St001863]], and let \operatorname{neg} be the number of negative entries, [[St001429]]. Then, $\operatorname{al}+\operatorname{cr}=(n-\operatorname{wex})(\operatorname{wex}-1+\operatorname{neg})+\binom{\operatorname{neg}{2}$.