searching the database
Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000114
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
St000114: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0]]
=> 1
[[1,0],[1]]
=> 2
[[2,0],[0]]
=> 2
[[2,0],[1]]
=> 3
[[2,0],[2]]
=> 4
[[1,1],[1]]
=> 3
[[1,0,0],[0,0],[0]]
=> 1
[[1,0,0],[1,0],[0]]
=> 2
[[1,0,0],[1,0],[1]]
=> 3
[[3,0],[0]]
=> 3
[[3,0],[1]]
=> 4
[[3,0],[2]]
=> 5
[[3,0],[3]]
=> 6
[[2,1],[1]]
=> 4
[[2,1],[2]]
=> 5
[[2,0,0],[0,0],[0]]
=> 2
[[2,0,0],[1,0],[0]]
=> 3
[[2,0,0],[1,0],[1]]
=> 4
[[2,0,0],[2,0],[0]]
=> 4
[[2,0,0],[2,0],[1]]
=> 5
[[2,0,0],[2,0],[2]]
=> 6
[[1,1,0],[1,0],[0]]
=> 3
[[1,1,0],[1,0],[1]]
=> 4
[[1,1,0],[1,1],[1]]
=> 5
[[1,0,0,0],[0,0,0],[0,0],[0]]
=> 1
[[1,0,0,0],[1,0,0],[0,0],[0]]
=> 2
[[1,0,0,0],[1,0,0],[1,0],[0]]
=> 3
[[1,0,0,0],[1,0,0],[1,0],[1]]
=> 4
[[4,0],[0]]
=> 4
[[4,0],[1]]
=> 5
[[4,0],[2]]
=> 6
[[4,0],[3]]
=> 7
[[4,0],[4]]
=> 8
[[3,1],[1]]
=> 5
[[3,1],[2]]
=> 6
[[3,1],[3]]
=> 7
[[2,2],[2]]
=> 6
[[3,0,0],[0,0],[0]]
=> 3
[[3,0,0],[1,0],[0]]
=> 4
[[3,0,0],[1,0],[1]]
=> 5
[[3,0,0],[2,0],[0]]
=> 5
[[3,0,0],[2,0],[1]]
=> 6
[[3,0,0],[2,0],[2]]
=> 7
[[3,0,0],[3,0],[0]]
=> 6
[[3,0,0],[3,0],[1]]
=> 7
[[3,0,0],[3,0],[2]]
=> 8
[[3,0,0],[3,0],[3]]
=> 9
[[2,1,0],[1,0],[0]]
=> 4
[[2,1,0],[1,0],[1]]
=> 5
[[2,1,0],[1,1],[1]]
=> 6
Description
The sum of the entries of the Gelfand-Tsetlin pattern.
Matching statistic: St000103
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
St000103: Semistandard tableaux ⟶ ℤResult quality: 72% ●values known / values provided: 72%●distinct values known / distinct values provided: 100%
St000103: Semistandard tableaux ⟶ ℤResult quality: 72% ●values known / values provided: 72%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0]]
=> [[2]]
=> ? = 2
[[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],[0,0],[0]]
=> [[3]]
=> ? ∊ {2,3}
[[1,0,0],[1,0],[0]]
=> [[2]]
=> ? ∊ {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],[0,0],[0]]
=> [[3,3]]
=> ? ∊ {4,4,5,5,6}
[[2,0,0],[1,0],[0]]
=> [[2,3]]
=> ? ∊ {4,4,5,5,6}
[[2,0,0],[1,0],[1]]
=> [[1,3]]
=> ? ∊ {4,4,5,5,6}
[[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],[1,0],[0]]
=> [[2],[3]]
=> ? ∊ {4,4,5,5,6}
[[1,1,0],[1,0],[1]]
=> [[1],[3]]
=> ? ∊ {4,4,5,5,6}
[[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> 3
[[1,0,0,0],[0,0,0],[0,0],[0]]
=> [[4]]
=> ? ∊ {2,3,4}
[[1,0,0,0],[1,0,0],[0,0],[0]]
=> [[3]]
=> ? ∊ {2,3,4}
[[1,0,0,0],[1,0,0],[1,0],[0]]
=> [[2]]
=> ? ∊ {2,3,4}
[[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],[0,0,0],[0,0],[0]]
=> [[4,4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[1,0,0],[0,0],[0]]
=> [[3,4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[1,0,0],[1,0],[0]]
=> [[2,4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[1,0,0],[1,0],[1]]
=> [[1,4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[2,0,0],[0,0],[0]]
=> [[3,3]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[2,0,0],[1,0],[0]]
=> [[2,3]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[2,0,0,0],[2,0,0],[1,0],[1]]
=> [[1,3]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[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],[1,0,0],[0,0],[0]]
=> [[3],[4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[1,1,0,0],[1,0,0],[1,0],[0]]
=> [[2],[4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[1,1,0,0],[1,0,0],[1,0],[1]]
=> [[1],[4]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[1,1,0,0],[1,1,0],[1,0],[0]]
=> [[2],[3]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[1,1,0,0],[1,1,0],[1,0],[1]]
=> [[1],[3]]
=> ? ∊ {4,4,5,5,5,5,6,6,6,7,7,8}
[[1,1,0,0],[1,1,0],[1,1],[1]]
=> [[1],[2]]
=> 3
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
=> [[5]]
=> ? ∊ {2,3,4,5}
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
=> [[4]]
=> ? ∊ {2,3,4,5}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
=> [[3]]
=> ? ∊ {2,3,4,5}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]]
=> [[2]]
=> ? ∊ {2,3,4,5}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
=> [[1]]
=> 1
[[3,0,0,0],[0,0,0],[0,0],[0]]
=> [[4,4,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[1,0,0],[0,0],[0]]
=> [[3,4,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[1,0,0],[1,0],[0]]
=> [[2,4,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[1,0,0],[1,0],[1]]
=> [[1,4,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[0,0],[0]]
=> [[3,3,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[1,0],[0]]
=> [[2,3,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[1,0],[1]]
=> [[1,3,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[2,0],[0]]
=> [[2,2,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[2,0],[1]]
=> [[1,2,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[3,0,0,0],[2,0,0],[2,0],[2]]
=> [[1,1,4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,0,0],[0,0],[0]]
=> [[3,4],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,0,0],[1,0],[0]]
=> [[2,4],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,0,0],[1,0],[1]]
=> [[1,4],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,1,0],[1,0],[0]]
=> [[2,4],[3]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,1,0],[1,0],[1]]
=> [[1,4],[3]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[1,1,0],[1,1],[1]]
=> [[1,4],[2]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[0,0],[0]]
=> [[3,3],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[1,0],[0]]
=> [[2,3],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[1,0],[1]]
=> [[1,3],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[2,0],[0]]
=> [[2,2],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[2,0],[1]]
=> [[1,2],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[2,1,0,0],[2,0,0],[2,0],[2]]
=> [[1,1],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
[[1,1,1,0],[1,1,0],[1,0],[0]]
=> [[2],[3],[4]]
=> ? ∊ {6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,12}
Description
The sum of the entries of a semistandard tableau.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!