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Matching statistic: St001882
Mapping
St001882: 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] => 0
[-1,-2] => 0
[2,1] => 0
[2,-1] => 1
[-2,1] => 0
[-2,-1] => 0
[1,2,3] => 0
[1,2,-3] => 2
[1,-2,3] => 1
[1,-2,-3] => 1
[-1,2,3] => 0
[-1,2,-3] => 2
[-1,-2,3] => 0
[-1,-2,-3] => 0
[1,3,2] => 0
[1,3,-2] => 2
[1,-3,2] => 1
[1,-3,-2] => 1
[-1,3,2] => 0
[-1,3,-2] => 1
[-1,-3,2] => 1
[-1,-3,-2] => 0
[2,1,3] => 0
[2,1,-3] => 2
[2,-1,3] => 1
[2,-1,-3] => 3
[-2,1,3] => 0
[-2,1,-3] => 1
[-2,-1,3] => 0
[-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] => 1
[-2,-3,1] => 0
[-2,-3,-1] => 0
[3,1,2] => 0
[3,1,-2] => 3
[3,-1,2] => 1
[3,-1,-2] => 1
[-3,1,2] => 0
[-3,1,-2] => 1
[-3,-1,2] => 0
[-3,-1,-2] => 0
Description
The number of occurrences of a type-B 231 pattern in a signed permutation. For a signed permutation $\pi\in\mathfrak H_n$, a triple $-n \leq i < j < k\leq n$ is an occurrence of the type-B $231$ pattern, if $1 \leq j < k$, $\pi(i) < \pi(j)$ and $\pi(i)$ is one larger than $\pi(k)$, i.e., $\pi(i) = \pi(k) + 1$ if $\pi(k) \neq -1$ and $\pi(i) = 1$ otherwise.