Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000103
(load all 4 compositions to match this statistic)
Mapping
St000103: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => 3
[[2,2]]
 => 4
[[1],[2]]
 => 3
[[1,1,2]]
 => 4
[[1,2,2]]
 => 5
[[2,2,2]]
 => 6
[[1,1],[2]]
 => 4
[[1,2],[2]]
 => 5
[[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
[[1,1,1,3]]
 => 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
Description
The sum of the entries of a semistandard tableau.
Matching statistic: St000114
(load all 4 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: 44% ●values known / values provided: 44%●distinct values known / distinct values provided: 74%
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
[[1,1,2]]
 => [[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
[[1,1,3]]
 => [[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
[[1,1,1,3]]
 => [[4,0,0],[3,0],[3]]
 => [[4,0,0],[1,0],[1]]
 => 6
[[1,1,2,3]]
 => [[4,0,0],[3,0],[2]]
 => [[4,0,0],[2,0],[1]]
 => 7
[[1,1,3,3]]
 => [[4,0,0],[2,0],[2]]
 => [[4,0,0],[2,0],[2]]
 => 8
[[1,2,2,3]]
 => [[4,0,0],[3,0],[1]]
 => [[4,0,0],[3,0],[1]]
 => 8
[[1,2,3,3]]
 => [[4,0,0],[2,0],[1]]
 => [[4,0,0],[3,0],[2]]
 => 9
[[1,3,3,3]]
 => [[4,0,0],[1,0],[1]]
 => [[4,0,0],[3,0],[3]]
 => 10
[[2,2,2,3]]
 => [[4,0,0],[3,0],[0]]
 => [[4,0,0],[4,0],[1]]
 => 9
[[2,2,3,3]]
 => [[4,0,0],[2,0],[0]]
 => [[4,0,0],[4,0],[2]]
 => 10
[[2,3,3,3]]
 => [[4,0,0],[1,0],[0]]
 => [[4,0,0],[4,0],[3]]
 => 11
[[3,3,3,3]]
 => [[4,0,0],[0,0],[0]]
 => [[4,0,0],[4,0],[4]]
 => 12
[[1,1,1],[3]]
 => [[3,1,0],[3,0],[3]]
 => [[3,1,0],[1,0],[1]]
 => 6
[[1,1,2],[3]]
 => [[3,1,0],[3,0],[2]]
 => [[3,1,0],[1,1],[1]]
 => 7
[[1,1,3],[2]]
 => [[3,1,0],[2,1],[2]]
 => [[3,1,0],[2,0],[1]]
 => 7
[[1,1,3],[3]]
 => [[3,1,0],[2,0],[2]]
 => [[3,1,0],[2,0],[2]]
 => 8
[[1,2,2],[3]]
 => [[3,1,0],[3,0],[1]]
 => [[3,1,0],[2,1],[1]]
 => 8
[[1,2,3],[2]]
 => [[3,1,0],[2,1],[1]]
 => [[3,1,0],[3,0],[1]]
 => 8
[[1,2,3],[3]]
 => [[3,1,0],[2,0],[1]]
 => [[3,1,0],[2,1],[2]]
 => 9
[[1,3,3],[2]]
 => [[3,1,0],[1,1],[1]]
 => [[3,1,0],[3,0],[2]]
 => 9
[[1,3,3],[3]]
 => [[3,1,0],[1,0],[1]]
 => [[3,1,0],[3,0],[3]]
 => 10
[[2,2,2],[3]]
 => [[3,1,0],[3,0],[0]]
 => [[3,1,0],[3,1],[1]]
 => 9
[[2,2,3],[3]]
 => [[3,1,0],[2,0],[0]]
 => [[3,1,0],[3,1],[2]]
 => 10
[[1,1,1,1,4]]
 => [[5,0,0,0],[4,0,0],[4,0],[4]]
 => [[5,0,0,0],[1,0,0],[1,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,1,2,4]]
 => [[5,0,0,0],[4,0,0],[4,0],[3]]
 => [[5,0,0,0],[2,0,0],[1,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,1,3,4]]
 => [[5,0,0,0],[4,0,0],[3,0],[3]]
 => [[5,0,0,0],[2,0,0],[2,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,1,4,4]]
 => [[5,0,0,0],[3,0,0],[3,0],[3]]
 => [[5,0,0,0],[2,0,0],[2,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,2,2,4]]
 => [[5,0,0,0],[4,0,0],[4,0],[2]]
 => [[5,0,0,0],[3,0,0],[1,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,2,3,4]]
 => [[5,0,0,0],[4,0,0],[3,0],[2]]
 => [[5,0,0,0],[3,0,0],[2,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,2,4,4]]
 => [[5,0,0,0],[3,0,0],[3,0],[2]]
 => [[5,0,0,0],[3,0,0],[2,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,3,3,4]]
 => [[5,0,0,0],[4,0,0],[2,0],[2]]
 => [[5,0,0,0],[3,0,0],[3,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,3,4,4]]
 => [[5,0,0,0],[3,0,0],[2,0],[2]]
 => [[5,0,0,0],[3,0,0],[3,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,4,4,4]]
 => [[5,0,0,0],[2,0,0],[2,0],[2]]
 => [[5,0,0,0],[3,0,0],[3,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,2,2,4]]
 => [[5,0,0,0],[4,0,0],[4,0],[1]]
 => [[5,0,0,0],[4,0,0],[1,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,2,3,4]]
 => [[5,0,0,0],[4,0,0],[3,0],[1]]
 => [[5,0,0,0],[4,0,0],[2,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,2,4,4]]
 => [[5,0,0,0],[3,0,0],[3,0],[1]]
 => [[5,0,0,0],[4,0,0],[2,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,3,3,4]]
 => [[5,0,0,0],[4,0,0],[2,0],[1]]
 => [[5,0,0,0],[4,0,0],[3,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,3,4,4]]
 => [[5,0,0,0],[3,0,0],[2,0],[1]]
 => [[5,0,0,0],[4,0,0],[3,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,2,4,4,4]]
 => [[5,0,0,0],[2,0,0],[2,0],[1]]
 => [[5,0,0,0],[4,0,0],[3,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,3,3,3,4]]
 => [[5,0,0,0],[4,0,0],[1,0],[1]]
 => [[5,0,0,0],[4,0,0],[4,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,3,3,4,4]]
 => [[5,0,0,0],[3,0,0],[1,0],[1]]
 => [[5,0,0,0],[4,0,0],[4,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,3,4,4,4]]
 => [[5,0,0,0],[2,0,0],[1,0],[1]]
 => [[5,0,0,0],[4,0,0],[4,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,4,4,4,4]]
 => [[5,0,0,0],[1,0,0],[1,0],[1]]
 => [[5,0,0,0],[4,0,0],[4,0],[4]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,2,2,4]]
 => [[5,0,0,0],[4,0,0],[4,0],[0]]
 => [[5,0,0,0],[5,0,0],[1,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,2,3,4]]
 => [[5,0,0,0],[4,0,0],[3,0],[0]]
 => [[5,0,0,0],[5,0,0],[2,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,2,4,4]]
 => [[5,0,0,0],[3,0,0],[3,0],[0]]
 => [[5,0,0,0],[5,0,0],[2,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,3,3,4]]
 => [[5,0,0,0],[4,0,0],[2,0],[0]]
 => [[5,0,0,0],[5,0,0],[3,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,3,4,4]]
 => [[5,0,0,0],[3,0,0],[2,0],[0]]
 => [[5,0,0,0],[5,0,0],[3,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,2,4,4,4]]
 => [[5,0,0,0],[2,0,0],[2,0],[0]]
 => [[5,0,0,0],[5,0,0],[3,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,3,3,3,4]]
 => [[5,0,0,0],[4,0,0],[1,0],[0]]
 => [[5,0,0,0],[5,0,0],[4,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,3,3,4,4]]
 => [[5,0,0,0],[3,0,0],[1,0],[0]]
 => [[5,0,0,0],[5,0,0],[4,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,3,4,4,4]]
 => [[5,0,0,0],[2,0,0],[1,0],[0]]
 => [[5,0,0,0],[5,0,0],[4,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[2,4,4,4,4]]
 => [[5,0,0,0],[1,0,0],[1,0],[0]]
 => [[5,0,0,0],[5,0,0],[4,0],[4]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[3,3,3,3,4]]
 => [[5,0,0,0],[4,0,0],[0,0],[0]]
 => [[5,0,0,0],[5,0,0],[5,0],[1]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[3,3,3,4,4]]
 => [[5,0,0,0],[3,0,0],[0,0],[0]]
 => [[5,0,0,0],[5,0,0],[5,0],[2]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[3,3,4,4,4]]
 => [[5,0,0,0],[2,0,0],[0,0],[0]]
 => [[5,0,0,0],[5,0,0],[5,0],[3]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[3,4,4,4,4]]
 => [[5,0,0,0],[1,0,0],[0,0],[0]]
 => [[5,0,0,0],[5,0,0],[5,0],[4]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[4,4,4,4,4]]
 => [[5,0,0,0],[0,0,0],[0,0],[0]]
 => [[5,0,0,0],[5,0,0],[5,0],[5]]
 => ? ∊ {8,9,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,20}
[[1,1,1,1,5]]
 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
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 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,2,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,2,5,5]]
 => [[5,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,3,3,5]]
 => [[5,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,3,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,3,5,5]]
 => [[5,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,4,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,4,5,5]]
 => [[5,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
[[1,1,5,5,5]]
 => [[5,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
 => ?
 => ? ∊ {9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,24,24,25}
Description
The sum of the entries of the Gelfand-Tsetlin pattern.
Matching statistic: St000716
(load all 2 compositions to match this statistic)
Mapping
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000716: Integer partitions ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 9%
Values
[[1,2]]
 => [[1,2]]
 => [2]
 => []
 => ? ∊ {3,3,4}
[[2,2]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {3,3,4}
[[1],[2]]
 => [[1,2]]
 => [2]
 => []
 => ? ∊ {3,3,4}
[[1,1,2]]
 => [[1,1,2]]
 => [3]
 => []
 => ? ∊ {4,4,5,5,6}
[[1,2,2]]
 => [[1,2,2]]
 => [3]
 => []
 => ? ∊ {4,4,5,5,6}
[[2,2,2]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {4,4,5,5,6}
[[1,1],[2]]
 => [[1,1,2]]
 => [3]
 => []
 => ? ∊ {4,4,5,5,6}
[[1,2],[2]]
 => [[1,2,2]]
 => [3]
 => []
 => ? ∊ {4,4,5,5,6}
[[1,1,3]]
 => [[1,1,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,2,3]]
 => [[1,2,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,3,3]]
 => [[1,3,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[2,2,3]]
 => [[2,2,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[2,3,3]]
 => [[2,3,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[3,3,3]]
 => [[3,3,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,1],[3]]
 => [[1,1,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,2],[3]]
 => [[1,2,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,3],[2]]
 => [[1,2],[3]]
 => [2,1]
 => [1]
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,3],[3]]
 => [[1,3,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[2,2],[3]]
 => [[2,2,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[2,3],[3]]
 => [[2,3,3]]
 => [3]
 => []
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1],[2],[3]]
 => [[1,2],[3]]
 => [2,1]
 => [1]
 => ? ∊ {5,5,6,6,6,6,7,7,7,7,8,8,9}
[[1,1,1,2]]
 => [[1,1,1,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,1,2,2]]
 => [[1,1,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,2,2,2]]
 => [[1,2,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[2,2,2,2]]
 => [[2,2,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,1,1],[2]]
 => [[1,1,1,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,1,2],[2]]
 => [[1,1,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,2,2],[2]]
 => [[1,2,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,1],[2,2]]
 => [[1,1,2,2]]
 => [4]
 => []
 => ? ∊ {5,5,6,6,6,7,7,8}
[[1,1,1,3]]
 => [[1,1,1,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,2,3]]
 => [[1,1,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,3,3]]
 => [[1,1,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,2,2,3]]
 => [[1,2,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,2,3,3]]
 => [[1,2,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,3,3,3]]
 => [[1,3,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[2,2,2,3]]
 => [[2,2,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[2,2,3,3]]
 => [[2,2,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[2,3,3,3]]
 => [[2,3,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[3,3,3,3]]
 => [[3,3,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,1],[3]]
 => [[1,1,1,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,2],[3]]
 => [[1,1,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,3],[2]]
 => [[1,1,2],[3]]
 => [3,1]
 => [1]
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,1,3],[3]]
 => [[1,1,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,2,2],[3]]
 => [[1,2,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,2,3],[2]]
 => [[1,2,2],[3]]
 => [3,1]
 => [1]
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,2,3],[3]]
 => [[1,2,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,3,3],[2]]
 => [[1,2,3],[3]]
 => [3,1]
 => [1]
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,3,3],[3]]
 => [[1,3,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[2,2,2],[3]]
 => [[2,2,2,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[2,2,3],[3]]
 => [[2,2,3,3]]
 => [4]
 => []
 => ? ∊ {6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12}
[[1,4],[2],[3]]
 => [[1,2],[3],[4]]
 => [2,1,1]
 => [1,1]
 => 14
[[1],[2],[3],[4]]
 => [[1,2],[3],[4]]
 => [2,1,1]
 => [1,1]
 => 14
[[1,1,4],[2],[3]]
 => [[1,1,2],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2,4],[2],[3]]
 => [[1,2,2],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3,4],[2],[3]]
 => [[1,2,3],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4,4],[2],[3]]
 => [[1,2,4],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1],[2],[3],[4]]
 => [[1,1,2],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2],[2],[3],[4]]
 => [[1,2,2],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3],[2],[3],[4]]
 => [[1,2,3],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4],[2],[3],[4]]
 => [[1,2,4],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3,5],[2,4]]
 => [[1,2,4],[3,5]]
 => [3,2]
 => [2]
 => 21
[[1,1,5],[2],[3]]
 => [[1,1,2],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1,5],[2],[4]]
 => [[1,1,2],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1,5],[3],[4]]
 => [[1,1,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2,5],[2],[3]]
 => [[1,2,2],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2,5],[2],[4]]
 => [[1,2,2],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3,5],[2],[3]]
 => [[1,2,3],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2,5],[3],[4]]
 => [[1,2,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3,5],[2],[4]]
 => [[1,2,4],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4,5],[2],[3]]
 => [[1,2,5],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5,5],[2],[3]]
 => [[1,2,5],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4,5],[2],[4]]
 => [[1,2,4],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5,5],[2],[4]]
 => [[1,2,5],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3,5],[3],[4]]
 => [[1,3,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4,5],[3],[4]]
 => [[1,3,4],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5,5],[3],[4]]
 => [[1,3,5],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,2,5],[3],[4]]
 => [[2,2,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,3,5],[3],[4]]
 => [[2,3,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,4,5],[3],[4]]
 => [[2,3,4],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,5,5],[3],[4]]
 => [[2,3,5],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3],[2,4],[5]]
 => [[1,2,4],[3,5]]
 => [3,2]
 => [2]
 => 21
[[1,4],[2,5],[3]]
 => [[1,2,5],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1],[2],[3],[5]]
 => [[1,1,2],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1],[2],[4],[5]]
 => [[1,1,2],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,1],[3],[4],[5]]
 => [[1,1,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2],[2],[3],[5]]
 => [[1,2,2],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2],[2],[4],[5]]
 => [[1,2,2],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3],[2],[3],[5]]
 => [[1,2,3],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,2],[3],[4],[5]]
 => [[1,2,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3],[2],[4],[5]]
 => [[1,2,4],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4],[2],[3],[5]]
 => [[1,2,5],[3],[4]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5],[2],[3],[4]]
 => [[1,2],[3],[4],[5]]
 => [2,1,1,1]
 => [1,1,1]
 => 14
[[1,5],[2],[3],[5]]
 => [[1,2,5],[3],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4],[2],[4],[5]]
 => [[1,2,4],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5],[2],[4],[5]]
 => [[1,2,5],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,3],[3],[4],[5]]
 => [[1,3,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,4],[3],[4],[5]]
 => [[1,3,4],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[1,5],[3],[4],[5]]
 => [[1,3,5],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,2],[3],[4],[5]]
 => [[2,2,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
[[2,3],[3],[4],[5]]
 => [[2,3,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => 14
Description
The dimension of the irreducible representation of Sp(6) labelled by an integer partition. Consider the symplectic group $Sp(2n)$. Then the integer partition $(\mu_1,\dots,\mu_k)$ of length at most $n$ corresponds to the weight vector $(\mu_1-\mu_2,\dots,\mu_{k-2}-\mu_{k-1},\mu_n,0,\dots,0)$. For example, the integer partition $(2)$ labels the symmetric square of the vector representation, whereas the integer partition $(1,1)$ labels the second fundamental representation.