Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000339
Mapping
St000339: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 3
[1,3,4,2] => 2
[1,4,2,3] => 1
[1,4,3,2] => 2
[2,1,3,4] => 5
[2,1,4,3] => 4
[2,3,1,4] => 5
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 4
[3,1,2,4] => 4
[3,1,4,2] => 4
[3,2,1,4] => 4
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 5
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 2
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 3
[1,2,4,5,3] => 2
[1,2,5,3,4] => 1
[1,2,5,4,3] => 2
[1,3,2,4,5] => 5
[1,3,2,5,4] => 4
[1,3,4,2,5] => 5
[1,3,4,5,2] => 3
[1,3,5,2,4] => 2
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 4
[1,4,3,2,5] => 4
[1,4,3,5,2] => 3
[1,4,5,2,3] => 2
Description
The maf index of a permutation. Let $\sigma$ be a permutation with fixed point set $\operatorname{FIX}(\sigma)$, and let $\operatorname{Der}(\sigma)$ be the derangement obtained from $\sigma$ by removing the fixed points. Then $$\operatorname{maf}(\sigma) = \sum_{i \in \operatorname{FIX}(\sigma)} i - \binom{|\operatorname{FIX}(\sigma)|+1}{2} + \operatorname{maj}(\operatorname{Der}(\sigma)),$$ where $\operatorname{maj}(\operatorname{Der}(\sigma))$ is the major index of the derangement of $\sigma$.