Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000020
Mapping
St000020: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 4
[3,1,2] => 5
[3,2,1] => 6
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 5
[1,4,3,2] => 6
[2,1,3,4] => 7
[2,1,4,3] => 8
[2,3,1,4] => 9
[2,3,4,1] => 10
[2,4,1,3] => 11
[2,4,3,1] => 12
[3,1,2,4] => 13
[3,1,4,2] => 14
[3,2,1,4] => 15
[3,2,4,1] => 16
[3,4,1,2] => 17
[3,4,2,1] => 18
[4,1,2,3] => 19
[4,1,3,2] => 20
[4,2,1,3] => 21
[4,2,3,1] => 22
[4,3,1,2] => 23
[4,3,2,1] => 24
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 5
[1,2,5,4,3] => 6
[1,3,2,4,5] => 7
[1,3,2,5,4] => 8
[1,3,4,2,5] => 9
[1,3,4,5,2] => 10
[1,3,5,2,4] => 11
[1,3,5,4,2] => 12
[1,4,2,3,5] => 13
[1,4,2,5,3] => 14
[1,4,3,2,5] => 15
[1,4,3,5,2] => 16
[1,4,5,2,3] => 17
Description
The rank of the permutation. This is its position among all permutations of the same size ordered lexicographically. This can be computed using the Lehmer code of a permutation: $$\text{rank}(\sigma) = 1 +\sum_{i=1}^{n-1} L(\sigma)_i (n − i)!,$$ where $L(\sigma)_i$ is the $i$-th entry of the Lehmer code of $\sigma$.