Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000059
Mapping
St000059: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 0
[[1,2]]
 => 0
[[1],[2]]
 => 1
[[1,2,3]]
 => 0
[[1,3],[2]]
 => 1
[[1,2],[3]]
 => 2
[[1],[2],[3]]
 => 3
[[1,2,3,4]]
 => 0
[[1,3,4],[2]]
 => 1
[[1,2,4],[3]]
 => 2
[[1,2,3],[4]]
 => 3
[[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => 4
[[1,4],[2],[3]]
 => 3
[[1,3],[2],[4]]
 => 4
[[1,2],[3],[4]]
 => 5
[[1],[2],[3],[4]]
 => 6
[[1,2,3,4,5]]
 => 0
[[1,3,4,5],[2]]
 => 1
[[1,2,4,5],[3]]
 => 2
[[1,2,3,5],[4]]
 => 3
[[1,2,3,4],[5]]
 => 4
[[1,3,5],[2,4]]
 => 2
[[1,2,5],[3,4]]
 => 4
[[1,3,4],[2,5]]
 => 3
[[1,2,4],[3,5]]
 => 5
[[1,2,3],[4,5]]
 => 6
[[1,4,5],[2],[3]]
 => 3
[[1,3,5],[2],[4]]
 => 4
[[1,2,5],[3],[4]]
 => 5
[[1,3,4],[2],[5]]
 => 5
[[1,2,4],[3],[5]]
 => 6
[[1,2,3],[4],[5]]
 => 7
[[1,4],[2,5],[3]]
 => 4
[[1,3],[2,5],[4]]
 => 5
[[1,2],[3,5],[4]]
 => 7
[[1,3],[2,4],[5]]
 => 6
[[1,2],[3,4],[5]]
 => 8
[[1,5],[2],[3],[4]]
 => 6
[[1,4],[2],[3],[5]]
 => 7
[[1,3],[2],[4],[5]]
 => 8
[[1,2],[3],[4],[5]]
 => 9
[[1],[2],[3],[4],[5]]
 => 10
[[1,2,3,4,5,6]]
 => 0
[[1,3,4,5,6],[2]]
 => 1
[[1,2,4,5,6],[3]]
 => 2
[[1,2,3,5,6],[4]]
 => 3
[[1,2,3,4,6],[5]]
 => 4
[[1,2,3,4,5],[6]]
 => 5
[[1,3,5,6],[2,4]]
 => 2
Description
The inversion number of a standard tableau as defined by Haglund and Stevens. Their inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b), where the inversion path is defined in detail in [1].