Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000170
Mapping
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000170: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [[1,2]]
 => 1
[[2,2]]
 => [[2,2]]
 => 2
[[1],[2]]
 => [[1,2]]
 => 1
[[1,3]]
 => [[1,3]]
 => 1
[[2,3]]
 => [[2,3]]
 => 2
[[3,3]]
 => [[3,3]]
 => 3
[[1],[3]]
 => [[1,3]]
 => 1
[[2],[3]]
 => [[2,3]]
 => 2
[[1,1,2]]
 => [[1,1,2]]
 => 1
[[1,2,2]]
 => [[1,2,2]]
 => 1
[[2,2,2]]
 => [[2,2,2]]
 => 2
[[1,1],[2]]
 => [[1,1,2]]
 => 1
[[1,2],[2]]
 => [[1,2,2]]
 => 1
[[1,4]]
 => [[1,4]]
 => 1
[[2,4]]
 => [[2,4]]
 => 2
[[3,4]]
 => [[3,4]]
 => 3
[[4,4]]
 => [[4,4]]
 => 4
[[1],[4]]
 => [[1,4]]
 => 1
[[2],[4]]
 => [[2,4]]
 => 2
[[3],[4]]
 => [[3,4]]
 => 3
[[1,1,3]]
 => [[1,1,3]]
 => 1
[[1,2,3]]
 => [[1,2,3]]
 => 1
[[1,3,3]]
 => [[1,3,3]]
 => 1
[[2,2,3]]
 => [[2,2,3]]
 => 2
[[2,3,3]]
 => [[2,3,3]]
 => 2
[[3,3,3]]
 => [[3,3,3]]
 => 3
[[1,1],[3]]
 => [[1,1,3]]
 => 1
[[1,2],[3]]
 => [[1,2,3]]
 => 1
[[1,3],[2]]
 => [[1,2],[3]]
 => 1
[[1,3],[3]]
 => [[1,3,3]]
 => 1
[[2,2],[3]]
 => [[2,2,3]]
 => 2
[[2,3],[3]]
 => [[2,3,3]]
 => 2
[[1],[2],[3]]
 => [[1,2],[3]]
 => 1
[[1,1,1,2]]
 => [[1,1,1,2]]
 => 1
[[1,1,2,2]]
 => [[1,1,2,2]]
 => 1
[[1,2,2,2]]
 => [[1,2,2,2]]
 => 1
[[2,2,2,2]]
 => [[2,2,2,2]]
 => 2
[[1,1,1],[2]]
 => [[1,1,1,2]]
 => 1
[[1,1,2],[2]]
 => [[1,1,2,2]]
 => 1
[[1,2,2],[2]]
 => [[1,2,2,2]]
 => 1
[[1,1],[2,2]]
 => [[1,1,2,2]]
 => 1
[[1,5]]
 => [[1,5]]
 => 1
[[2,5]]
 => [[2,5]]
 => 2
[[3,5]]
 => [[3,5]]
 => 3
[[4,5]]
 => [[4,5]]
 => 4
[[5,5]]
 => [[5,5]]
 => 5
[[1],[5]]
 => [[1,5]]
 => 1
[[2],[5]]
 => [[2,5]]
 => 2
[[3],[5]]
 => [[3,5]]
 => 3
[[4],[5]]
 => [[4,5]]
 => 4
Description
The trace of a semistandard tableau. This is the sum of the entries on the diagonal.
Matching statistic: St001410
(load all 4 compositions to match this statistic)
Mapping
St001410: Semistandard tableaux ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 86%
Values
[[1,2]]
 => 1
[[2,2]]
 => 2
[[1],[2]]
 => 1
[[1,3]]
 => 1
[[2,3]]
 => 2
[[3,3]]
 => 3
[[1],[3]]
 => 1
[[2],[3]]
 => 2
[[1,1,2]]
 => 1
[[1,2,2]]
 => 1
[[2,2,2]]
 => 2
[[1,1],[2]]
 => 1
[[1,2],[2]]
 => 1
[[1,4]]
 => 1
[[2,4]]
 => 2
[[3,4]]
 => 3
[[4,4]]
 => 4
[[1],[4]]
 => 1
[[2],[4]]
 => 2
[[3],[4]]
 => 3
[[1,1,3]]
 => 1
[[1,2,3]]
 => 1
[[1,3,3]]
 => 1
[[2,2,3]]
 => 2
[[2,3,3]]
 => 2
[[3,3,3]]
 => 3
[[1,1],[3]]
 => 1
[[1,2],[3]]
 => 1
[[1,3],[2]]
 => 1
[[1,3],[3]]
 => 1
[[2,2],[3]]
 => 2
[[2,3],[3]]
 => 2
[[1],[2],[3]]
 => 1
[[1,1,1,2]]
 => 1
[[1,1,2,2]]
 => 1
[[1,2,2,2]]
 => 1
[[2,2,2,2]]
 => 2
[[1,1,1],[2]]
 => 1
[[1,1,2],[2]]
 => 1
[[1,2,2],[2]]
 => 1
[[1,1],[2,2]]
 => 1
[[1,5]]
 => 1
[[2,5]]
 => 2
[[3,5]]
 => 3
[[4,5]]
 => 4
[[5,5]]
 => 5
[[1],[5]]
 => 1
[[2],[5]]
 => 2
[[3],[5]]
 => 3
[[4],[5]]
 => 4
[[1,1,1,2,3],[2]]
 => ? = 1
[[1,1,1,3,3],[2]]
 => ? = 1
[[1,1,2,2,3],[2]]
 => ? = 1
[[1,1,2,3,3],[2]]
 => ? = 1
[[1,1,3,3,3],[2]]
 => ? = 1
[[1,2,2,3,3],[2]]
 => ? = 1
[[1,2,3,3,3],[2]]
 => ? = 1
[[1,1,1,3],[2,2]]
 => ? = 1
[[1,1,1,3],[2,3]]
 => ? = 1
[[1,1,2,3],[2,2]]
 => ? = 1
[[1,1,2,3],[2,3]]
 => ? = 1
[[1,1,3,3],[2,3]]
 => ? = 1
[[1,2,2,3],[2,3]]
 => ? = 1
[[1,2,3,3],[2,3]]
 => ? = 1
[[1,1,1,2],[2],[3]]
 => ? = 1
[[1,1,1,3],[2],[3]]
 => ? = 1
[[1,1,2,2],[2],[3]]
 => ? = 1
[[1,1,2,3],[2],[3]]
 => ? = 1
[[1,1,3,3],[2],[3]]
 => ? = 1
[[1,2,2,3],[2],[3]]
 => ? = 1
[[1,2,3,3],[2],[3]]
 => ? = 1
[[1,1,1],[2,2],[3]]
 => ? = 1
[[1,1,1],[2,3],[3]]
 => ? = 1
[[1,1,2],[2,2],[3]]
 => ? = 1
[[1,1,2],[2,3],[3]]
 => ? = 1
[[1,1,3],[2,3],[3]]
 => ? = 1
[[1,2,2],[2,3],[3]]
 => ? = 1
[[1,2,3],[2,3],[3]]
 => ? = 1
[[1,2,3,4,5]]
 => ? = 1
[[1,2,3,4],[5]]
 => ? = 1
[[1,2,3,5],[4]]
 => ? = 1
[[1,2,4,5],[3]]
 => ? = 1
[[1,3,4,5],[2]]
 => ? = 1
[[1,2,3],[4,5]]
 => ? = 1
[[1,2,4],[3,5]]
 => ? = 1
[[1,2,5],[3,4]]
 => ? = 1
[[1,3,4],[2,5]]
 => ? = 1
[[1,3,5],[2,4]]
 => ? = 6
[[1,2,3],[4],[5]]
 => ? = 1
[[1,2,4],[3],[5]]
 => ? = 1
[[1,2,5],[3],[4]]
 => ? = 1
[[1,3,4],[2],[5]]
 => ? = 1
[[1,3,5],[2],[4]]
 => ? = 1
[[1,4,5],[2],[3]]
 => ? = 1
[[1,2],[3,4],[5]]
 => ? = 1
[[1,2],[3,5],[4]]
 => ? = 1
[[1,3],[2,4],[5]]
 => ? = 6
[[1,3],[2,5],[4]]
 => ? = 1
[[1,4],[2,5],[3]]
 => ? = 1
[[1,2],[3],[4],[5]]
 => ? = 1
Description
The minimal entry of a semistandard tableau.