Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000462
Mapping
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000462: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => {{1,2}}
 => [2,1] => 0
[[1],[2]]
 => {{1},{2}}
 => [1,2] => 0
[[1,2,3]]
 => {{1,2,3}}
 => [2,3,1] => 0
[[1,3],[2]]
 => {{1,3},{2}}
 => [3,2,1] => 2
[[1,2],[3]]
 => {{1,2},{3}}
 => [2,1,3] => 0
[[1],[2],[3]]
 => {{1},{2},{3}}
 => [1,2,3] => 0
[[1,2,3,4]]
 => {{1,2,3,4}}
 => [2,3,4,1] => 0
[[1,3,4],[2]]
 => {{1,3,4},{2}}
 => [3,2,4,1] => 2
[[1,2,4],[3]]
 => {{1,2,4},{3}}
 => [2,4,3,1] => 3
[[1,2,3],[4]]
 => {{1,2,3},{4}}
 => [2,3,1,4] => 0
[[1,3],[2,4]]
 => {{1,3},{2,4}}
 => [3,4,1,2] => 0
[[1,2],[3,4]]
 => {{1,2},{3,4}}
 => [2,1,4,3] => 2
[[1,4],[2],[3]]
 => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[[1,3],[2],[4]]
 => {{1,3},{2},{4}}
 => [3,2,1,4] => 2
[[1,2],[3],[4]]
 => {{1,2},{3},{4}}
 => [2,1,3,4] => 0
[[1],[2],[3],[4]]
 => {{1},{2},{3},{4}}
 => [1,2,3,4] => 0
[[1,2,3,4,5]]
 => {{1,2,3,4,5}}
 => [2,3,4,5,1] => 0
[[1,3,4,5],[2]]
 => {{1,3,4,5},{2}}
 => [3,2,4,5,1] => 2
[[1,2,4,5],[3]]
 => {{1,2,4,5},{3}}
 => [2,4,3,5,1] => 3
[[1,2,3,5],[4]]
 => {{1,2,3,5},{4}}
 => [2,3,5,4,1] => 4
[[1,2,3,4],[5]]
 => {{1,2,3,4},{5}}
 => [2,3,4,1,5] => 0
[[1,3,5],[2,4]]
 => {{1,3,5},{2,4}}
 => [3,4,5,2,1] => 4
[[1,2,5],[3,4]]
 => {{1,2,5},{3,4}}
 => [2,5,4,3,1] => 6
[[1,3,4],[2,5]]
 => {{1,3,4},{2,5}}
 => [3,5,4,1,2] => 2
[[1,2,4],[3,5]]
 => {{1,2,4},{3,5}}
 => [2,4,5,1,3] => 0
[[1,2,3],[4,5]]
 => {{1,2,3},{4,5}}
 => [2,3,1,5,4] => 3
[[1,4,5],[2],[3]]
 => {{1,4,5},{2},{3}}
 => [4,2,3,5,1] => 3
[[1,3,5],[2],[4]]
 => {{1,3,5},{2},{4}}
 => [3,2,5,4,1] => 6
[[1,2,5],[3],[4]]
 => {{1,2,5},{3},{4}}
 => [2,5,3,4,1] => 4
[[1,3,4],[2],[5]]
 => {{1,3,4},{2},{5}}
 => [3,2,4,1,5] => 2
[[1,2,4],[3],[5]]
 => {{1,2,4},{3},{5}}
 => [2,4,3,1,5] => 3
[[1,2,3],[4],[5]]
 => {{1,2,3},{4},{5}}
 => [2,3,1,4,5] => 0
[[1,4],[2,5],[3]]
 => {{1,4},{2,5},{3}}
 => [4,5,3,1,2] => 3
[[1,3],[2,5],[4]]
 => {{1,3},{2,5},{4}}
 => [3,5,1,4,2] => 4
[[1,2],[3,5],[4]]
 => {{1,2},{3,5},{4}}
 => [2,1,5,4,3] => 6
[[1,3],[2,4],[5]]
 => {{1,3},{2,4},{5}}
 => [3,4,1,2,5] => 0
[[1,2],[3,4],[5]]
 => {{1,2},{3,4},{5}}
 => [2,1,4,3,5] => 2
[[1,5],[2],[3],[4]]
 => {{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => 4
[[1,4],[2],[3],[5]]
 => {{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => 3
[[1,3],[2],[4],[5]]
 => {{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => 2
[[1,2],[3],[4],[5]]
 => {{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => 0
[[1],[2],[3],[4],[5]]
 => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => 0
[[1,2,3,4,5,6]]
 => {{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => 0
[[1,3,4,5,6],[2]]
 => {{1,3,4,5,6},{2}}
 => [3,2,4,5,6,1] => 2
[[1,2,4,5,6],[3]]
 => {{1,2,4,5,6},{3}}
 => [2,4,3,5,6,1] => 3
[[1,2,3,5,6],[4]]
 => {{1,2,3,5,6},{4}}
 => [2,3,5,4,6,1] => 4
[[1,2,3,4,6],[5]]
 => {{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => 5
[[1,2,3,4,5],[6]]
 => {{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => 0
[[1,3,5,6],[2,4]]
 => {{1,3,5,6},{2,4}}
 => [3,4,5,2,6,1] => 4
[[1,2,5,6],[3,4]]
 => {{1,2,5,6},{3,4}}
 => [2,5,4,3,6,1] => 6
Description
The major index minus the number of excedences of a permutation. This occurs in the context of Eulerian polynomials [1].