Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000114
(load all 2 compositions to match this statistic)
Mapping
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00078: Gelfand-Tsetlin patterns —Schuetzenberger involution⟶ Gelfand-Tsetlin patterns
St000114: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [[2,0],[1]]
 => [[2,0],[1]]
 => 3
[[2,2]]
 => [[2,0],[0]]
 => [[2,0],[2]]
 => 4
[[1],[2]]
 => [[1,1],[1]]
 => [[1,1],[1]]
 => 3
[[1,3]]
 => [[2,0,0],[1,0],[1]]
 => [[2,0,0],[1,0],[1]]
 => 4
[[2,3]]
 => [[2,0,0],[1,0],[0]]
 => [[2,0,0],[2,0],[1]]
 => 5
[[3,3]]
 => [[2,0,0],[0,0],[0]]
 => [[2,0,0],[2,0],[2]]
 => 6
[[1],[3]]
 => [[1,1,0],[1,0],[1]]
 => [[1,1,0],[1,0],[1]]
 => 4
[[2],[3]]
 => [[1,1,0],[1,0],[0]]
 => [[1,1,0],[1,1],[1]]
 => 5
[[1,1,2]]
 => [[3,0],[2]]
 => [[3,0],[1]]
 => 4
[[1,2,2]]
 => [[3,0],[1]]
 => [[3,0],[2]]
 => 5
[[2,2,2]]
 => [[3,0],[0]]
 => [[3,0],[3]]
 => 6
[[1,1],[2]]
 => [[2,1],[2]]
 => [[2,1],[1]]
 => 4
[[1,2],[2]]
 => [[2,1],[1]]
 => [[2,1],[2]]
 => 5
[[1,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[2,0,0,0],[1,0,0],[1,0],[1]]
 => 5
[[2,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,0,0,0],[2,0,0],[1,0],[1]]
 => 6
[[3,4]]
 => [[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[2,0,0,0],[2,0,0],[2,0],[1]]
 => 7
[[4,4]]
 => [[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[2,0,0,0],[2,0,0],[2,0],[2]]
 => 8
[[1],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[1]]
 => [[1,1,0,0],[1,0,0],[1,0],[1]]
 => 5
[[2],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[0]]
 => [[1,1,0,0],[1,1,0],[1,0],[1]]
 => 6
[[3],[4]]
 => [[1,1,0,0],[1,0,0],[0,0],[0]]
 => [[1,1,0,0],[1,1,0],[1,1],[1]]
 => 7
[[1,1,3]]
 => [[3,0,0],[2,0],[2]]
 => [[3,0,0],[1,0],[1]]
 => 5
[[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => [[3,0,0],[2,0],[1]]
 => 6
[[1,3,3]]
 => [[3,0,0],[1,0],[1]]
 => [[3,0,0],[2,0],[2]]
 => 7
[[2,2,3]]
 => [[3,0,0],[2,0],[0]]
 => [[3,0,0],[3,0],[1]]
 => 7
[[2,3,3]]
 => [[3,0,0],[1,0],[0]]
 => [[3,0,0],[3,0],[2]]
 => 8
[[3,3,3]]
 => [[3,0,0],[0,0],[0]]
 => [[3,0,0],[3,0],[3]]
 => 9
[[1,1],[3]]
 => [[2,1,0],[2,0],[2]]
 => [[2,1,0],[1,0],[1]]
 => 5
[[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => [[2,1,0],[1,1],[1]]
 => 6
[[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => [[2,1,0],[2,0],[1]]
 => 6
[[1,3],[3]]
 => [[2,1,0],[1,0],[1]]
 => [[2,1,0],[2,0],[2]]
 => 7
[[2,2],[3]]
 => [[2,1,0],[2,0],[0]]
 => [[2,1,0],[2,1],[1]]
 => 7
[[2,3],[3]]
 => [[2,1,0],[1,0],[0]]
 => [[2,1,0],[2,1],[2]]
 => 8
[[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => [[1,1,1],[1,1],[1]]
 => 6
[[1,1,1,2]]
 => [[4,0],[3]]
 => [[4,0],[1]]
 => 5
[[1,1,2,2]]
 => [[4,0],[2]]
 => [[4,0],[2]]
 => 6
[[1,2,2,2]]
 => [[4,0],[1]]
 => [[4,0],[3]]
 => 7
[[2,2,2,2]]
 => [[4,0],[0]]
 => [[4,0],[4]]
 => 8
[[1,1,1],[2]]
 => [[3,1],[3]]
 => [[3,1],[1]]
 => 5
[[1,1,2],[2]]
 => [[3,1],[2]]
 => [[3,1],[2]]
 => 6
[[1,2,2],[2]]
 => [[3,1],[1]]
 => [[3,1],[3]]
 => 7
[[1,1],[2,2]]
 => [[2,2],[2]]
 => [[2,2],[2]]
 => 6
[[1,5]]
 => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => 6
[[2,5]]
 => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]]
 => 7
[[3,5]]
 => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]]
 => 8
[[4,5]]
 => [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
 => 9
[[5,5]]
 => [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
 => 10
[[1],[5]]
 => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => 6
[[2],[5]]
 => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]]
 => 7
[[3],[5]]
 => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]]
 => 8
[[4],[5]]
 => [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => 9
Description
The sum of the entries of the Gelfand-Tsetlin pattern.
Matching statistic: St000103
(load all 4 compositions to match this statistic)
Mapping
St000103: Semistandard tableaux ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 63%
Values
[[1,2]]
 => 3
[[2,2]]
 => 4
[[1],[2]]
 => 3
[[1,3]]
 => ? = 4
[[2,3]]
 => ? = 5
[[3,3]]
 => ? = 6
[[1],[3]]
 => ? = 4
[[2],[3]]
 => ? = 5
[[1,1,2]]
 => 4
[[1,2,2]]
 => 5
[[2,2,2]]
 => 6
[[1,1],[2]]
 => 4
[[1,2],[2]]
 => 5
[[1,4]]
 => ? = 5
[[2,4]]
 => ? = 6
[[3,4]]
 => ? = 7
[[4,4]]
 => ? = 8
[[1],[4]]
 => ? = 5
[[2],[4]]
 => ? = 6
[[3],[4]]
 => ? = 7
[[1,1,3]]
 => 5
[[1,2,3]]
 => 6
[[1,3,3]]
 => 7
[[2,2,3]]
 => 7
[[2,3,3]]
 => 8
[[3,3,3]]
 => 9
[[1,1],[3]]
 => 5
[[1,2],[3]]
 => 6
[[1,3],[2]]
 => 6
[[1,3],[3]]
 => 7
[[2,2],[3]]
 => 7
[[2,3],[3]]
 => 8
[[1],[2],[3]]
 => 6
[[1,1,1,2]]
 => 5
[[1,1,2,2]]
 => 6
[[1,2,2,2]]
 => 7
[[2,2,2,2]]
 => 8
[[1,1,1],[2]]
 => 5
[[1,1,2],[2]]
 => 6
[[1,2,2],[2]]
 => 7
[[1,1],[2,2]]
 => 6
[[1,5]]
 => ? = 6
[[2,5]]
 => ? = 7
[[3,5]]
 => ? = 8
[[4,5]]
 => ? = 9
[[5,5]]
 => ? = 10
[[1],[5]]
 => ? = 6
[[2],[5]]
 => ? = 7
[[3],[5]]
 => ? = 8
[[4],[5]]
 => ? = 9
[[1,1,4]]
 => ? = 6
[[1,2,4]]
 => ? = 7
[[1,3,4]]
 => ? = 8
[[1,4,4]]
 => ? = 9
[[2,2,4]]
 => ? = 8
[[2,3,4]]
 => ? = 9
[[2,4,4]]
 => ? = 10
[[3,3,4]]
 => ? = 10
[[3,4,4]]
 => ? = 11
[[4,4,4]]
 => ? = 12
[[1,1],[4]]
 => ? = 6
[[1,2],[4]]
 => ? = 7
[[1,4],[2]]
 => ? = 7
[[1,3],[4]]
 => ? = 8
[[1,4],[3]]
 => ? = 8
[[1,4],[4]]
 => ? = 9
[[2,2],[4]]
 => ? = 8
[[2,3],[4]]
 => ? = 9
[[2,4],[3]]
 => ? = 9
[[2,4],[4]]
 => ? = 10
[[3,3],[4]]
 => ? = 10
[[3,4],[4]]
 => ? = 11
[[1],[2],[4]]
 => ? = 7
[[1],[3],[4]]
 => ? = 8
[[2],[3],[4]]
 => ? = 9
[[1,1,1,3]]
 => 6
[[1,1,2,3]]
 => 7
[[1,1,3,3]]
 => 8
[[1,2,2,3]]
 => 8
[[1,2,3,3]]
 => 9
[[1,3,3,3]]
 => 10
[[2,2,2,3]]
 => 9
[[2,2,3,3]]
 => 10
[[2,3,3,3]]
 => 11
[[3,3,3,3]]
 => 12
[[1,1,1],[3]]
 => 6
[[1,1,2],[3]]
 => 7
[[1,1,3],[2]]
 => 7
[[1,1,3],[3]]
 => 8
[[1,2,2],[3]]
 => 8
[[1,2,3],[2]]
 => 8
[[1,2,3],[3]]
 => 9
[[1,3,3],[2]]
 => 9
[[1,3,3],[3]]
 => 10
[[2,2,2],[3]]
 => 9
[[2,2,3],[3]]
 => 10
[[1,6]]
 => ? = 7
[[2,6]]
 => ? = 8
[[3,6]]
 => ? = 9
[[4,6]]
 => ? = 10
Description
The sum of the entries of a semistandard tableau.