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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000103
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Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
St000103: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000103: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0],[1]]
=> [[1]]
=> 1
[[2,0],[0]]
=> [[2,2]]
=> 4
[[2,0],[1]]
=> [[1,2]]
=> 3
[[2,0],[2]]
=> [[1,1]]
=> 2
[[1,1],[1]]
=> [[1],[2]]
=> 3
[[1,0,0],[1,0],[1]]
=> [[1]]
=> 1
[[3,0],[0]]
=> [[2,2,2]]
=> 6
[[3,0],[1]]
=> [[1,2,2]]
=> 5
[[3,0],[2]]
=> [[1,1,2]]
=> 4
[[3,0],[3]]
=> [[1,1,1]]
=> 3
[[2,1],[1]]
=> [[1,2],[2]]
=> 5
[[2,1],[2]]
=> [[1,1],[2]]
=> 4
[[2,0,0],[2,0],[0]]
=> [[2,2]]
=> 4
[[2,0,0],[2,0],[1]]
=> [[1,2]]
=> 3
[[2,0,0],[2,0],[2]]
=> [[1,1]]
=> 2
[[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> 3
[[1,0,0,0],[1,0,0],[1,0],[1]]
=> [[1]]
=> 1
[[4,0],[0]]
=> [[2,2,2,2]]
=> 8
[[4,0],[1]]
=> [[1,2,2,2]]
=> 7
[[4,0],[2]]
=> [[1,1,2,2]]
=> 6
[[4,0],[3]]
=> [[1,1,1,2]]
=> 5
[[4,0],[4]]
=> [[1,1,1,1]]
=> 4
[[3,1],[1]]
=> [[1,2,2],[2]]
=> 7
[[3,1],[2]]
=> [[1,1,2],[2]]
=> 6
[[3,1],[3]]
=> [[1,1,1],[2]]
=> 5
[[2,2],[2]]
=> [[1,1],[2,2]]
=> 6
[[3,0,0],[0,0],[0]]
=> [[3,3,3]]
=> 9
[[3,0,0],[1,0],[0]]
=> [[2,3,3]]
=> 8
[[3,0,0],[1,0],[1]]
=> [[1,3,3]]
=> 7
[[3,0,0],[2,0],[0]]
=> [[2,2,3]]
=> 7
[[3,0,0],[2,0],[1]]
=> [[1,2,3]]
=> 6
[[3,0,0],[2,0],[2]]
=> [[1,1,3]]
=> 5
[[3,0,0],[3,0],[0]]
=> [[2,2,2]]
=> 6
[[3,0,0],[3,0],[1]]
=> [[1,2,2]]
=> 5
[[3,0,0],[3,0],[2]]
=> [[1,1,2]]
=> 4
[[3,0,0],[3,0],[3]]
=> [[1,1,1]]
=> 3
[[2,1,0],[1,0],[0]]
=> [[2,3],[3]]
=> 8
[[2,1,0],[1,0],[1]]
=> [[1,3],[3]]
=> 7
[[2,1,0],[1,1],[1]]
=> [[1,3],[2]]
=> 6
[[2,1,0],[2,0],[0]]
=> [[2,2],[3]]
=> 7
[[2,1,0],[2,0],[1]]
=> [[1,2],[3]]
=> 6
[[2,1,0],[2,0],[2]]
=> [[1,1],[3]]
=> 5
[[2,1,0],[2,1],[1]]
=> [[1,2],[2]]
=> 5
[[2,1,0],[2,1],[2]]
=> [[1,1],[2]]
=> 4
[[1,1,1],[1,1],[1]]
=> [[1],[2],[3]]
=> 6
[[2,0,0,0],[2,0,0],[2,0],[0]]
=> [[2,2]]
=> 4
[[2,0,0,0],[2,0,0],[2,0],[1]]
=> [[1,2]]
=> 3
[[2,0,0,0],[2,0,0],[2,0],[2]]
=> [[1,1]]
=> 2
[[1,1,0,0],[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> 3
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
=> [[1]]
=> 1
Description
The sum of the entries of a semistandard tableau.
Matching statistic: St000114
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Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
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: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 95%
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: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 95%
Values
[[1,0],[1]]
=> [[1]]
=> [[1]]
=> [[1]]
=> 1
[[2,0],[0]]
=> [[2,2]]
=> [[2,0],[0]]
=> [[2,0],[2]]
=> 4
[[2,0],[1]]
=> [[1,2]]
=> [[2,0],[1]]
=> [[2,0],[1]]
=> 3
[[2,0],[2]]
=> [[1,1]]
=> [[2]]
=> [[2]]
=> 2
[[1,1],[1]]
=> [[1],[2]]
=> [[1,1],[1]]
=> [[1,1],[1]]
=> 3
[[1,0,0],[1,0],[1]]
=> [[1]]
=> [[1]]
=> [[1]]
=> 1
[[3,0],[0]]
=> [[2,2,2]]
=> [[3,0],[0]]
=> [[3,0],[3]]
=> 6
[[3,0],[1]]
=> [[1,2,2]]
=> [[3,0],[1]]
=> [[3,0],[2]]
=> 5
[[3,0],[2]]
=> [[1,1,2]]
=> [[3,0],[2]]
=> [[3,0],[1]]
=> 4
[[3,0],[3]]
=> [[1,1,1]]
=> [[3]]
=> [[3]]
=> 3
[[2,1],[1]]
=> [[1,2],[2]]
=> [[2,1],[1]]
=> [[2,1],[2]]
=> 5
[[2,1],[2]]
=> [[1,1],[2]]
=> [[2,1],[2]]
=> [[2,1],[1]]
=> 4
[[2,0,0],[2,0],[0]]
=> [[2,2]]
=> [[2,0],[0]]
=> [[2,0],[2]]
=> 4
[[2,0,0],[2,0],[1]]
=> [[1,2]]
=> [[2,0],[1]]
=> [[2,0],[1]]
=> 3
[[2,0,0],[2,0],[2]]
=> [[1,1]]
=> [[2]]
=> [[2]]
=> 2
[[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> [[1,1],[1]]
=> [[1,1],[1]]
=> 3
[[1,0,0,0],[1,0,0],[1,0],[1]]
=> [[1]]
=> [[1]]
=> [[1]]
=> 1
[[4,0],[0]]
=> [[2,2,2,2]]
=> [[4,0],[0]]
=> [[4,0],[4]]
=> 8
[[4,0],[1]]
=> [[1,2,2,2]]
=> [[4,0],[1]]
=> [[4,0],[3]]
=> 7
[[4,0],[2]]
=> [[1,1,2,2]]
=> [[4,0],[2]]
=> [[4,0],[2]]
=> 6
[[4,0],[3]]
=> [[1,1,1,2]]
=> [[4,0],[3]]
=> [[4,0],[1]]
=> 5
[[4,0],[4]]
=> [[1,1,1,1]]
=> [[4]]
=> [[4]]
=> 4
[[3,1],[1]]
=> [[1,2,2],[2]]
=> [[3,1],[1]]
=> [[3,1],[3]]
=> 7
[[3,1],[2]]
=> [[1,1,2],[2]]
=> [[3,1],[2]]
=> [[3,1],[2]]
=> 6
[[3,1],[3]]
=> [[1,1,1],[2]]
=> [[3,1],[3]]
=> [[3,1],[1]]
=> 5
[[2,2],[2]]
=> [[1,1],[2,2]]
=> [[2,2],[2]]
=> [[2,2],[2]]
=> 6
[[3,0,0],[0,0],[0]]
=> [[3,3,3]]
=> [[3,0,0],[0,0],[0]]
=> [[3,0,0],[3,0],[3]]
=> 9
[[3,0,0],[1,0],[0]]
=> [[2,3,3]]
=> [[3,0,0],[1,0],[0]]
=> [[3,0,0],[3,0],[2]]
=> 8
[[3,0,0],[1,0],[1]]
=> [[1,3,3]]
=> [[3,0,0],[1,0],[1]]
=> [[3,0,0],[2,0],[2]]
=> 7
[[3,0,0],[2,0],[0]]
=> [[2,2,3]]
=> [[3,0,0],[2,0],[0]]
=> [[3,0,0],[3,0],[1]]
=> 7
[[3,0,0],[2,0],[1]]
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> [[3,0,0],[2,0],[1]]
=> 6
[[3,0,0],[2,0],[2]]
=> [[1,1,3]]
=> [[3,0,0],[2,0],[2]]
=> [[3,0,0],[1,0],[1]]
=> 5
[[3,0,0],[3,0],[0]]
=> [[2,2,2]]
=> [[3,0],[0]]
=> [[3,0],[3]]
=> 6
[[3,0,0],[3,0],[1]]
=> [[1,2,2]]
=> [[3,0],[1]]
=> [[3,0],[2]]
=> 5
[[3,0,0],[3,0],[2]]
=> [[1,1,2]]
=> [[3,0],[2]]
=> [[3,0],[1]]
=> 4
[[3,0,0],[3,0],[3]]
=> [[1,1,1]]
=> [[3]]
=> [[3]]
=> 3
[[2,1,0],[1,0],[0]]
=> [[2,3],[3]]
=> [[2,1,0],[1,0],[0]]
=> [[2,1,0],[2,1],[2]]
=> 8
[[2,1,0],[1,0],[1]]
=> [[1,3],[3]]
=> [[2,1,0],[1,0],[1]]
=> [[2,1,0],[2,0],[2]]
=> 7
[[2,1,0],[1,1],[1]]
=> [[1,3],[2]]
=> [[2,1,0],[1,1],[1]]
=> [[2,1,0],[2,0],[1]]
=> 6
[[2,1,0],[2,0],[0]]
=> [[2,2],[3]]
=> [[2,1,0],[2,0],[0]]
=> [[2,1,0],[2,1],[1]]
=> 7
[[2,1,0],[2,0],[1]]
=> [[1,2],[3]]
=> [[2,1,0],[2,0],[1]]
=> [[2,1,0],[1,1],[1]]
=> 6
[[2,1,0],[2,0],[2]]
=> [[1,1],[3]]
=> [[2,1,0],[2,0],[2]]
=> [[2,1,0],[1,0],[1]]
=> 5
[[2,1,0],[2,1],[1]]
=> [[1,2],[2]]
=> [[2,1],[1]]
=> [[2,1],[2]]
=> 5
[[2,1,0],[2,1],[2]]
=> [[1,1],[2]]
=> [[2,1],[2]]
=> [[2,1],[1]]
=> 4
[[1,1,1],[1,1],[1]]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> [[1,1,1],[1,1],[1]]
=> 6
[[2,0,0,0],[2,0,0],[2,0],[0]]
=> [[2,2]]
=> [[2,0],[0]]
=> [[2,0],[2]]
=> 4
[[2,0,0,0],[2,0,0],[2,0],[1]]
=> [[1,2]]
=> [[2,0],[1]]
=> [[2,0],[1]]
=> 3
[[2,0,0,0],[2,0,0],[2,0],[2]]
=> [[1,1]]
=> [[2]]
=> [[2]]
=> 2
[[1,1,0,0],[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> [[1,1],[1]]
=> [[1,1],[1]]
=> 3
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
=> [[1]]
=> [[1]]
=> [[1]]
=> 1
[[5,0,0,0],[0,0,0],[0,0],[0]]
=> [[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]]
=> ? = 20
[[5,0,0,0],[1,0,0],[0,0],[0]]
=> [[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]]
=> ? = 19
[[5,0,0,0],[1,0,0],[1,0],[0]]
=> [[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]]
=> ? = 18
[[5,0,0,0],[1,0,0],[1,0],[1]]
=> [[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]]
=> ? = 17
[[5,0,0,0],[2,0,0],[0,0],[0]]
=> [[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]]
=> ? = 18
[[5,0,0,0],[2,0,0],[1,0],[0]]
=> [[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]]
=> ? = 17
[[5,0,0,0],[2,0,0],[1,0],[1]]
=> [[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]]
=> ? = 16
[[5,0,0,0],[2,0,0],[2,0],[0]]
=> [[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]]
=> ? = 16
[[5,0,0,0],[2,0,0],[2,0],[1]]
=> [[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]]
=> ? = 15
[[5,0,0,0],[2,0,0],[2,0],[2]]
=> [[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]]
=> ? = 14
[[5,0,0,0],[3,0,0],[0,0],[0]]
=> [[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]]
=> ? = 17
[[5,0,0,0],[3,0,0],[1,0],[0]]
=> [[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]]
=> ? = 16
[[5,0,0,0],[3,0,0],[1,0],[1]]
=> [[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]]
=> ? = 15
[[5,0,0,0],[3,0,0],[2,0],[0]]
=> [[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]]
=> ? = 15
[[5,0,0,0],[3,0,0],[2,0],[1]]
=> [[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]]
=> ? = 14
[[5,0,0,0],[3,0,0],[2,0],[2]]
=> [[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]]
=> ? = 13
[[5,0,0,0],[3,0,0],[3,0],[0]]
=> [[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]]
=> ? = 14
[[5,0,0,0],[3,0,0],[3,0],[1]]
=> [[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]]
=> ? = 13
[[5,0,0,0],[3,0,0],[3,0],[2]]
=> [[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]]
=> ? = 12
[[5,0,0,0],[3,0,0],[3,0],[3]]
=> [[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]]
=> ? = 11
[[5,0,0,0],[4,0,0],[0,0],[0]]
=> [[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]]
=> ? = 16
[[5,0,0,0],[4,0,0],[1,0],[0]]
=> [[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]]
=> ? = 15
[[5,0,0,0],[4,0,0],[1,0],[1]]
=> [[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]]
=> ? = 14
[[5,0,0,0],[4,0,0],[2,0],[0]]
=> [[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]]
=> ? = 14
[[5,0,0,0],[4,0,0],[2,0],[1]]
=> [[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]]
=> ? = 13
[[5,0,0,0],[4,0,0],[2,0],[2]]
=> [[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]]
=> ? = 12
[[5,0,0,0],[4,0,0],[3,0],[0]]
=> [[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]]
=> ? = 13
[[5,0,0,0],[4,0,0],[3,0],[1]]
=> [[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]]
=> ? = 12
[[5,0,0,0],[4,0,0],[3,0],[2]]
=> [[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]]
=> ? = 11
[[5,0,0,0],[4,0,0],[3,0],[3]]
=> [[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]]
=> ? = 10
[[5,0,0,0],[4,0,0],[4,0],[0]]
=> [[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]]
=> ? = 12
[[5,0,0,0],[4,0,0],[4,0],[1]]
=> [[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]]
=> ? = 11
[[5,0,0,0],[4,0,0],[4,0],[2]]
=> [[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]]
=> ? = 10
[[5,0,0,0],[4,0,0],[4,0],[3]]
=> [[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]]
=> ? = 9
[[5,0,0,0],[4,0,0],[4,0],[4]]
=> [[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
Description
The sum of the entries of the Gelfand-Tsetlin pattern.
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