Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000231
Mapping
St000231: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => 2
{{1},{2}}
 => 3
{{1,2,3}}
 => 3
{{1,2},{3}}
 => 5
{{1,3},{2}}
 => 5
{{1},{2,3}}
 => 4
{{1},{2},{3}}
 => 6
{{1,2,3,4}}
 => 4
{{1,2,3},{4}}
 => 7
{{1,2,4},{3}}
 => 7
{{1,2},{3,4}}
 => 6
{{1,2},{3},{4}}
 => 9
{{1,3,4},{2}}
 => 6
{{1,3},{2,4}}
 => 7
{{1,3},{2},{4}}
 => 9
{{1,4},{2,3}}
 => 7
{{1},{2,3,4}}
 => 5
{{1},{2,3},{4}}
 => 8
{{1,4},{2},{3}}
 => 9
{{1},{2,4},{3}}
 => 8
{{1},{2},{3,4}}
 => 7
{{1},{2},{3},{4}}
 => 10
Description
Sum of the maximal elements of the blocks of a set partition.
Matching statistic: St001406
Mapping
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St001406: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [[1,2]]
 => [[2,0],[1]]
 => 2
{{1},{2}}
 => [[1],[2]]
 => [[1,1],[1]]
 => 3
{{1,2,3}}
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 3
{{1,2},{3}}
 => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 4
{{1,3},{2}}
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 5
{{1},{2,3}}
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 5
{{1},{2},{3}}
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 6
{{1,2,3,4}}
 => [[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => 4
{{1,2,3},{4}}
 => [[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 5
{{1,2,4},{3}}
 => [[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 6
{{1,2},{3,4}}
 => [[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => 6
{{1,2},{3},{4}}
 => [[1,2],[3],[4]]
 => [[2,1,1,0],[2,1,0],[2,0],[1]]
 => 7
{{1,3,4},{2}}
 => [[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 7
{{1,3},{2,4}}
 => [[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 7
{{1,3},{2},{4}}
 => [[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => 8
{{1,4},{2,3}}
 => [[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 7
{{1},{2,3,4}}
 => [[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 7
{{1},{2,3},{4}}
 => [[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => 8
{{1,4},{2},{3}}
 => [[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => 9
{{1},{2,4},{3}}
 => [[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => 9
{{1},{2},{3,4}}
 => [[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => 9
{{1},{2},{3},{4}}
 => [[1],[2],[3],[4]]
 => [[1,1,1,1],[1,1,1],[1,1],[1]]
 => 10
Description
The number of nonzero entries in a Gelfand Tsetlin pattern.
Matching statistic: St001645
(load all 9 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 44%
Values
{{1,2}}
 => [2,1] => [2,1] => ([(0,1)],2)
 => 2
{{1},{2}}
 => [1,2] => [1,2] => ([],2)
 => ? = 3
{{1,2,3}}
 => [2,3,1] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {5,5,6}
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {5,5,6}
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 4
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {5,5,6}
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,2,3},{4}}
 => [2,3,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,2},{3,4}}
 => [2,1,4,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,3,4},{2}}
 => [3,2,4,1] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,3},{2,4}}
 => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 8
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
{{1},{2,3,4}}
 => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 8
{{1},{2,3},{4}}
 => [1,3,2,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1},{2},{3,4}}
 => [1,2,4,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {5,6,6,7,7,7,7,7,9,9,9,10}
Description
The pebbling number of a connected graph.