Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000958
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Mapping
St000958: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 4
[1,2,3,4] => 1
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 4
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 6
[2,4,1,3] => 6
[2,4,3,1] => 16
[3,1,2,4] => 2
[3,1,4,2] => 6
[3,2,1,4] => 4
[3,2,4,1] => 16
[3,4,1,2] => 20
[3,4,2,1] => 52
[4,1,2,3] => 6
[4,1,3,2] => 16
[4,2,1,3] => 16
[4,2,3,1] => 64
[4,3,1,2] => 52
[4,3,2,1] => 168
[1,2,3,4,5] => 1
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 4
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 6
[1,3,5,2,4] => 6
[1,3,5,4,2] => 16
[1,4,2,3,5] => 2
[1,4,2,5,3] => 6
[1,4,3,2,5] => 4
[1,4,3,5,2] => 16
[1,4,5,2,3] => 20
Description
The number of Bruhat factorizations of a permutation. This is the number of factorizations $\pi = t_1 \cdots t_\ell$ for transpositions $\{ t_i \mid 1 \leq i \leq \ell\}$ such that the number of inversions of $t_1 \cdots t_i$ equals $i$ for all $1 \leq i \leq \ell$.