searching the database
Your data matches 4 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: St000231
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
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
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00215: Set partitions —Wachs-White⟶ Set partitions
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%
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}}
=> [[1,2]]
=> [[2,0],[1]]
=> 2
{{1},{2}}
=> {{1},{2}}
=> [[1],[2]]
=> [[1,1],[1]]
=> 3
{{1,2,3}}
=> {{1,2,3}}
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> 3
{{1,2},{3}}
=> {{1},{2,3}}
=> [[1,3],[2]]
=> [[2,1,0],[1,1],[1]]
=> 5
{{1,3},{2}}
=> {{1,3},{2}}
=> [[1,3],[2]]
=> [[2,1,0],[1,1],[1]]
=> 5
{{1},{2,3}}
=> {{1,2},{3}}
=> [[1,2],[3]]
=> [[2,1,0],[2,0],[1]]
=> 4
{{1},{2},{3}}
=> {{1},{2},{3}}
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 6
{{1,2,3,4}}
=> {{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}}
=> [[1,3,4],[2]]
=> [[3,1,0,0],[2,1,0],[1,1],[1]]
=> 7
{{1,2,4},{3}}
=> {{1,3},{2,4}}
=> [[1,3],[2,4]]
=> [[2,2,0,0],[2,1,0],[1,1],[1]]
=> 7
{{1,2},{3,4}}
=> {{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}}
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> 9
{{1,3,4},{2}}
=> {{1,2,4},{3}}
=> [[1,2,4],[3]]
=> [[3,1,0,0],[2,1,0],[2,0],[1]]
=> 6
{{1,3},{2,4}}
=> {{1,3,4},{2}}
=> [[1,3,4],[2]]
=> [[3,1,0,0],[2,1,0],[1,1],[1]]
=> 7
{{1,3},{2},{4}}
=> {{1},{2,4},{3}}
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> 9
{{1,4},{2,3}}
=> {{1,4},{2,3}}
=> [[1,3],[2,4]]
=> [[2,2,0,0],[2,1,0],[1,1],[1]]
=> 7
{{1},{2,3,4}}
=> {{1,2,3},{4}}
=> [[1,2,3],[4]]
=> [[3,1,0,0],[3,0,0],[2,0],[1]]
=> 5
{{1},{2,3},{4}}
=> {{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}}
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> 9
{{1},{2,4},{3}}
=> {{1,3},{2},{4}}
=> [[1,3],[2],[4]]
=> [[2,1,1,0],[2,1,0],[1,1],[1]]
=> 8
{{1},{2},{3,4}}
=> {{1,2},{3},{4}}
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> 7
{{1},{2},{3},{4}}
=> {{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
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 33%
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 33%
Values
{{1,2}}
=> [2] => [1,1] => ([(0,1)],2)
=> 2
{{1},{2}}
=> [1,1] => [2] => ([],2)
=> ? = 3
{{1,2,3}}
=> [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
{{1,2},{3}}
=> [2,1] => [1,2] => ([(1,2)],3)
=> ? = 5
{{1,3},{2}}
=> [2,1] => [1,2] => ([(1,2)],3)
=> ? = 5
{{1},{2,3}}
=> [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4
{{1},{2},{3}}
=> [1,1,1] => [3] => ([],3)
=> ? = 6
{{1,2,3,4}}
=> [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
{{1,2,3},{4}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 7
{{1,2,4},{3}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 7
{{1,2},{3,4}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 6
{{1,2},{3},{4}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? = 9
{{1,3,4},{2}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 6
{{1,3},{2,4}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 7
{{1,3},{2},{4}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? = 9
{{1,4},{2,3}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 7
{{1},{2,3,4}}
=> [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 5
{{1},{2,3},{4}}
=> [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 8
{{1,4},{2},{3}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? = 9
{{1},{2,4},{3}}
=> [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 8
{{1},{2},{3,4}}
=> [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 7
{{1},{2},{3},{4}}
=> [1,1,1,1] => [4] => ([],4)
=> ? = 10
Description
The pebbling number of a connected graph.
Matching statistic: St001060
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 22%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 22%
Values
{{1,2}}
=> [2] => [1] => ([],1)
=> ? = 2 - 5
{{1},{2}}
=> [1,1] => [2] => ([],2)
=> ? = 3 - 5
{{1,2,3}}
=> [3] => [1] => ([],1)
=> ? = 3 - 5
{{1,2},{3}}
=> [2,1] => [1,1] => ([(0,1)],2)
=> ? = 5 - 5
{{1,3},{2}}
=> [2,1] => [1,1] => ([(0,1)],2)
=> ? = 5 - 5
{{1},{2,3}}
=> [1,2] => [1,1] => ([(0,1)],2)
=> ? = 4 - 5
{{1},{2},{3}}
=> [1,1,1] => [3] => ([],3)
=> ? = 6 - 5
{{1,2,3,4}}
=> [4] => [1] => ([],1)
=> ? = 4 - 5
{{1,2,3},{4}}
=> [3,1] => [1,1] => ([(0,1)],2)
=> ? = 7 - 5
{{1,2,4},{3}}
=> [3,1] => [1,1] => ([(0,1)],2)
=> ? = 7 - 5
{{1,2},{3,4}}
=> [2,2] => [2] => ([],2)
=> ? = 6 - 5
{{1,2},{3},{4}}
=> [2,1,1] => [1,2] => ([(1,2)],3)
=> ? = 9 - 5
{{1,3,4},{2}}
=> [3,1] => [1,1] => ([(0,1)],2)
=> ? = 6 - 5
{{1,3},{2,4}}
=> [2,2] => [2] => ([],2)
=> ? = 7 - 5
{{1,3},{2},{4}}
=> [2,1,1] => [1,2] => ([(1,2)],3)
=> ? = 9 - 5
{{1,4},{2,3}}
=> [2,2] => [2] => ([],2)
=> ? = 7 - 5
{{1},{2,3,4}}
=> [1,3] => [1,1] => ([(0,1)],2)
=> ? = 5 - 5
{{1},{2,3},{4}}
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 8 - 5
{{1,4},{2},{3}}
=> [2,1,1] => [1,2] => ([(1,2)],3)
=> ? = 9 - 5
{{1},{2,4},{3}}
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 8 - 5
{{1},{2},{3,4}}
=> [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 7 - 5
{{1},{2},{3},{4}}
=> [1,1,1,1] => [4] => ([],4)
=> ? = 10 - 5
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
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!