Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001698
Mapping
St001698: 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]]
 => 0
[[1,2,3]]
 => 0
[[1,3],[2]]
 => 1
[[1,2],[3]]
 => 0
[[1],[2],[3]]
 => 0
[[1,2,3,4]]
 => 0
[[1,3,4],[2]]
 => 2
[[1,2,4],[3]]
 => 1
[[1,2,3],[4]]
 => 0
[[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => 0
[[1,4],[2],[3]]
 => 2
[[1,3],[2],[4]]
 => 1
[[1,2],[3],[4]]
 => 0
[[1],[2],[3],[4]]
 => 0
[[1,2,3,4,5]]
 => 0
[[1,3,4,5],[2]]
 => 3
[[1,2,4,5],[3]]
 => 2
[[1,2,3,5],[4]]
 => 1
[[1,2,3,4],[5]]
 => 0
[[1,3,5],[2,4]]
 => 4
[[1,2,5],[3,4]]
 => 1
[[1,3,4],[2,5]]
 => 3
[[1,2,4],[3,5]]
 => 2
[[1,2,3],[4,5]]
 => 0
[[1,4,5],[2],[3]]
 => 4
[[1,3,5],[2],[4]]
 => 3
[[1,2,5],[3],[4]]
 => 2
[[1,3,4],[2],[5]]
 => 2
[[1,2,4],[3],[5]]
 => 1
[[1,2,3],[4],[5]]
 => 0
[[1,4],[2,5],[3]]
 => 4
[[1,3],[2,5],[4]]
 => 2
[[1,2],[3,5],[4]]
 => 1
[[1,3],[2,4],[5]]
 => 3
[[1,2],[3,4],[5]]
 => 0
[[1,5],[2],[3],[4]]
 => 3
[[1,4],[2],[3],[5]]
 => 2
[[1,3],[2],[4],[5]]
 => 1
[[1,2],[3],[4],[5]]
 => 0
[[1],[2],[3],[4],[5]]
 => 0
[[1,2,3,4,5,6]]
 => 0
[[1,3,4,5,6],[2]]
 => 4
[[1,2,4,5,6],[3]]
 => 3
[[1,2,3,5,6],[4]]
 => 2
[[1,2,3,4,6],[5]]
 => 1
[[1,2,3,4,5],[6]]
 => 0
[[1,3,5,6],[2,4]]
 => 6
Description
The comajor index of a standard tableau minus the weighted size of its shape.
Matching statistic: St001699
Mapping
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
St001699: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [[1]]
 => 0
[[1,2]]
 => [[1,2]]
 => 0
[[1],[2]]
 => [[1],[2]]
 => 0
[[1,2,3]]
 => [[1,2,3]]
 => 0
[[1,3],[2]]
 => [[1,2],[3]]
 => 1
[[1,2],[3]]
 => [[1,3],[2]]
 => 0
[[1],[2],[3]]
 => [[1],[2],[3]]
 => 0
[[1,2,3,4]]
 => [[1,2,3,4]]
 => 0
[[1,3,4],[2]]
 => [[1,2,3],[4]]
 => 2
[[1,2,4],[3]]
 => [[1,2,4],[3]]
 => 1
[[1,2,3],[4]]
 => [[1,3,4],[2]]
 => 0
[[1,3],[2,4]]
 => [[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => [[1,2],[3,4]]
 => 0
[[1,4],[2],[3]]
 => [[1,2],[3],[4]]
 => 2
[[1,3],[2],[4]]
 => [[1,3],[2],[4]]
 => 1
[[1,2],[3],[4]]
 => [[1,4],[2],[3]]
 => 0
[[1],[2],[3],[4]]
 => [[1],[2],[3],[4]]
 => 0
[[1,2,3,4,5]]
 => [[1,2,3,4,5]]
 => 0
[[1,3,4,5],[2]]
 => [[1,2,3,4],[5]]
 => 3
[[1,2,4,5],[3]]
 => [[1,2,3,5],[4]]
 => 2
[[1,2,3,5],[4]]
 => [[1,2,4,5],[3]]
 => 1
[[1,2,3,4],[5]]
 => [[1,3,4,5],[2]]
 => 0
[[1,3,5],[2,4]]
 => [[1,2,4],[3,5]]
 => 4
[[1,2,5],[3,4]]
 => [[1,2,3],[4,5]]
 => 1
[[1,3,4],[2,5]]
 => [[1,3,4],[2,5]]
 => 3
[[1,2,4],[3,5]]
 => [[1,3,5],[2,4]]
 => 2
[[1,2,3],[4,5]]
 => [[1,2,5],[3,4]]
 => 0
[[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 4
[[1,3,5],[2],[4]]
 => [[1,2,4],[3],[5]]
 => 3
[[1,2,5],[3],[4]]
 => [[1,2,5],[3],[4]]
 => 2
[[1,3,4],[2],[5]]
 => [[1,3,4],[2],[5]]
 => 2
[[1,2,4],[3],[5]]
 => [[1,3,5],[2],[4]]
 => 1
[[1,2,3],[4],[5]]
 => [[1,4,5],[2],[3]]
 => 0
[[1,4],[2,5],[3]]
 => [[1,3],[2,4],[5]]
 => 4
[[1,3],[2,5],[4]]
 => [[1,2],[3,4],[5]]
 => 2
[[1,2],[3,5],[4]]
 => [[1,2],[3,5],[4]]
 => 1
[[1,3],[2,4],[5]]
 => [[1,4],[2,5],[3]]
 => 3
[[1,2],[3,4],[5]]
 => [[1,3],[2,5],[4]]
 => 0
[[1,5],[2],[3],[4]]
 => [[1,2],[3],[4],[5]]
 => 3
[[1,4],[2],[3],[5]]
 => [[1,3],[2],[4],[5]]
 => 2
[[1,3],[2],[4],[5]]
 => [[1,4],[2],[3],[5]]
 => 1
[[1,2],[3],[4],[5]]
 => [[1,5],[2],[3],[4]]
 => 0
[[1],[2],[3],[4],[5]]
 => [[1],[2],[3],[4],[5]]
 => 0
[[1,2,3,4,5,6]]
 => [[1,2,3,4,5,6]]
 => 0
[[1,3,4,5,6],[2]]
 => [[1,2,3,4,5],[6]]
 => 4
[[1,2,4,5,6],[3]]
 => [[1,2,3,4,6],[5]]
 => 3
[[1,2,3,5,6],[4]]
 => [[1,2,3,5,6],[4]]
 => 2
[[1,2,3,4,6],[5]]
 => [[1,2,4,5,6],[3]]
 => 1
[[1,2,3,4,5],[6]]
 => [[1,3,4,5,6],[2]]
 => 0
[[1,3,5,6],[2,4]]
 => [[1,2,3,5],[4,6]]
 => 6
Description
The major index of a standard tableau minus the weighted size of its shape.