Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000616
Mapping
St000616: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 5
[3,1,2] => 6
[3,2,1] => 8
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 7
[1,4,2,3] => 8
[1,4,3,2] => 11
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 5
[2,3,4,1] => 9
[2,4,1,3] => 10
[2,4,3,1] => 13
[3,1,2,4] => 6
[3,1,4,2] => 10
[3,2,1,4] => 8
[3,2,4,1] => 12
[3,4,1,2] => 14
[3,4,2,1] => 16
[4,1,2,3] => 12
[4,1,3,2] => 15
[4,2,1,3] => 14
[4,2,3,1] => 17
[4,3,1,2] => 18
[4,3,2,1] => 20
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 9
[1,2,5,3,4] => 10
[1,2,5,4,3] => 14
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 7
[1,3,4,5,2] => 12
[1,3,5,2,4] => 13
[1,3,5,4,2] => 17
[1,4,2,3,5] => 8
[1,4,2,5,3] => 13
[1,4,3,2,5] => 11
[1,4,3,5,2] => 16
[1,4,5,2,3] => 18
Description
The inversion index of a permutation. The ''inversion index'' of a permutation $\sigma=\sigma_1\sigma_2\ldots\sigma_n$ is defined as $$ \sum_{\mbox{inversion pairs } (\sigma_i,\sigma_j)} \sigma_i $$ where $(\sigma_i,\sigma_j)$ is an inversion pair if i < j and $\sigma_i > \sigma_j$. This equals the sum of the entries in the corresponding descending plane partition; see [1].