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Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000574
St000574: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 0
{{1},{2}}
=> 1
{{1,2,3}}
=> 0
{{1,2},{3}}
=> 1
{{1,3},{2}}
=> 2
{{1},{2,3}}
=> 1
{{1},{2},{3}}
=> 3
{{1,2,3,4}}
=> 0
{{1,2,3},{4}}
=> 1
{{1,2,4},{3}}
=> 2
{{1,2},{3,4}}
=> 1
{{1,2},{3},{4}}
=> 3
{{1,3,4},{2}}
=> 2
{{1,3},{2,4}}
=> 2
{{1,3},{2},{4}}
=> 4
{{1,4},{2,3}}
=> 2
{{1},{2,3,4}}
=> 1
{{1},{2,3},{4}}
=> 3
{{1,4},{2},{3}}
=> 5
{{1},{2,4},{3}}
=> 4
{{1},{2},{3,4}}
=> 3
{{1},{2},{3},{4}}
=> 6
{{1,2,3,4,5}}
=> 0
{{1,2,3,4},{5}}
=> 1
{{1,2,3,5},{4}}
=> 2
{{1,2,3},{4,5}}
=> 1
{{1,2,3},{4},{5}}
=> 3
{{1,2,4,5},{3}}
=> 2
{{1,2,4},{3,5}}
=> 2
{{1,2,4},{3},{5}}
=> 4
{{1,2,5},{3,4}}
=> 2
{{1,2},{3,4,5}}
=> 1
{{1,2},{3,4},{5}}
=> 3
{{1,2,5},{3},{4}}
=> 5
{{1,2},{3,5},{4}}
=> 4
{{1,2},{3},{4,5}}
=> 3
{{1,2},{3},{4},{5}}
=> 6
{{1,3,4,5},{2}}
=> 2
{{1,3,4},{2,5}}
=> 2
{{1,3,4},{2},{5}}
=> 4
{{1,3,5},{2,4}}
=> 2
{{1,3},{2,4,5}}
=> 2
{{1,3},{2,4},{5}}
=> 4
{{1,3,5},{2},{4}}
=> 5
{{1,3},{2,5},{4}}
=> 5
{{1,3},{2},{4,5}}
=> 4
{{1,3},{2},{4},{5}}
=> 7
{{1,4,5},{2,3}}
=> 2
{{1,4},{2,3,5}}
=> 2
{{1,4},{2,3},{5}}
=> 4
Description
The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element.
This is the number of pairs $i\lt j$ in different blocks such that $i$ is the minimal and $j$ is the maximal element of a block.
Matching statistic: St000456
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 86%
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 86%
Values
{{1,2}}
=> [2] => [1,1] => ([(0,1)],2)
=> 1
{{1},{2}}
=> [1,1] => [2] => ([],2)
=> ? = 0
{{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)
=> ? ∊ {0,1,2}
{{1,3},{2}}
=> [2,1] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,1,2}
{{1},{2,3}}
=> [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
{{1},{2},{3}}
=> [1,1,1] => [3] => ([],3)
=> ? ∊ {0,1,2}
{{1,2,3,4}}
=> [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
{{1,2,3},{4}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,2,4},{3}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,2},{3,4}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
{{1,2},{3},{4}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,3,4},{2}}
=> [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,3},{2,4}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
{{1,3},{2},{4}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,4},{2,3}}
=> [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
{{1},{2,3,4}}
=> [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
{{1},{2,3},{4}}
=> [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,4},{2},{3}}
=> [2,1,1] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1},{2,4},{3}}
=> [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1},{2},{3,4}}
=> [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1},{2},{3},{4}}
=> [1,1,1,1] => [4] => ([],4)
=> ? ∊ {0,1,1,2,3,3,3,4,5}
{{1,2,3,4,5}}
=> [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 10
{{1,2,3,4},{5}}
=> [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,3,5},{4}}
=> [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,3},{4,5}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,2,3},{4},{5}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,4,5},{3}}
=> [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,4},{3,5}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,2,4},{3},{5}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,5},{3,4}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,2},{3,4,5}}
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
{{1,2},{3,4},{5}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,5},{3},{4}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2},{3,5},{4}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2},{3},{4,5}}
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,2},{3},{4},{5}}
=> [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3,4,5},{2}}
=> [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3,4},{2,5}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,3,4},{2},{5}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3,5},{2,4}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,3},{2,4,5}}
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
{{1,3},{2,4},{5}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3,5},{2},{4}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3},{2,5},{4}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,3},{2},{4,5}}
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,3},{2},{4},{5}}
=> [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,4,5},{2,3}}
=> [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
{{1,4},{2,3,5}}
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
{{1,4},{2,3},{5}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,5},{2,3,4}}
=> [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
{{1},{2,3,4,5}}
=> [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
{{1},{2,3,4},{5}}
=> [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,5},{2,3},{4}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2,3,5},{4}}
=> [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2,3},{4,5}}
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
{{1},{2,3},{4},{5}}
=> [1,2,1,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,4,5},{2},{3}}
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,4},{2,5},{3}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,4},{2},{3,5}}
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,4},{2},{3},{5}}
=> [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,5},{2,4},{3}}
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2,4,5},{3}}
=> [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2,4},{3,5}}
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
{{1},{2,4},{3},{5}}
=> [1,2,1,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,5},{2},{3,4}}
=> [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1},{2,5},{3,4}}
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
{{1},{2},{3,4,5}}
=> [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
{{1},{2},{3,4},{5}}
=> [1,1,2,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,5},{2},{3},{4}}
=> [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2,5},{3},{4}}
=> [1,2,1,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2},{3,5},{4}}
=> [1,1,2,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1},{2},{3},{4,5}}
=> [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1},{2},{3},{4},{5}}
=> [1,1,1,1,1] => [5] => ([],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6,7,7,7,8,9}
{{1,2,3,4,5,6}}
=> [6] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 15
{{1,2,3,4,5},{6}}
=> [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3,4,6},{5}}
=> [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3,4},{5,6}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,3,4},{5},{6}}
=> [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3,5,6},{4}}
=> [5,1] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3,5},{4,6}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,3,5},{4},{6}}
=> [4,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3,6},{4,5}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,3},{4,5,6}}
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 9
{{1,2,3},{4,5},{6}}
=> [3,2,1] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,10,10,10,10,10,10,10,11,12,12,12,13,14}
{{1,2,3},{4},{5,6}}
=> [3,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
{{1,2,4,5},{3,6}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,4,6},{3,5}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,4},{3,5,6}}
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 9
{{1,2,4},{3},{5,6}}
=> [3,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
{{1,2,5,6},{3,4}}
=> [4,2] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
{{1,2,5},{3,4,6}}
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 9
{{1,2,6},{3,4,5}}
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 9
{{1,2},{3,4,5,6}}
=> [2,4] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 11
{{1,2},{3,4},{5,6}}
=> [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5
{{1,2,5},{3},{4,6}}
=> [3,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
{{1,2},{3,5},{4,6}}
=> [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5
{{1,2,6},{3},{4,5}}
=> [3,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
{{1,2},{3,6},{4,5}}
=> [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5
{{1,2},{3},{4,5,6}}
=> [2,1,3] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 7
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St000454
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 18%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 18%
Values
{{1,2}}
=> [2,1] => ([],2)
=> ([],2)
=> 0
{{1},{2}}
=> [1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1
{{1,2,3}}
=> [2,3,1] => ([(1,2)],3)
=> ([(1,2)],3)
=> 1
{{1,2},{3}}
=> [2,1,3] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> ? ∊ {1,2,3}
{{1,3},{2}}
=> [3,2,1] => ([],3)
=> ([],3)
=> 0
{{1},{2,3}}
=> [1,3,2] => ([(0,1),(0,2)],3)
=> ([(0,2),(1,2)],3)
=> ? ∊ {1,2,3}
{{1},{2},{3}}
=> [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> ? ∊ {1,2,3}
{{1,2,3,4}}
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,2,3},{4}}
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,2,4},{3}}
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,2},{3,4}}
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
{{1,2},{3},{4}}
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,3,4},{2}}
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,3},{2,4}}
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> 1
{{1,3},{2},{4}}
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,4},{2,3}}
=> [4,3,2,1] => ([],4)
=> ([],4)
=> 0
{{1},{2,3,4}}
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1},{2,3},{4}}
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
{{1,4},{2},{3}}
=> [4,2,3,1] => ([(2,3)],4)
=> ([(2,3)],4)
=> 1
{{1},{2,4},{3}}
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1},{2},{3,4}}
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1},{2},{3},{4}}
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {1,2,2,3,3,3,4,4,5,6}
{{1,2,3,4,5}}
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 2
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 2
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => ([(3,4)],5)
=> ([(3,4)],5)
=> 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> 1
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => ([],5)
=> ([],5)
=> 0
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ([(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => ([(1,5),(5,2),(5,3),(5,4)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> 2
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
{{1,2,5,6},{3},{4}}
=> [2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> 2
{{1,2,6},{3,5},{4}}
=> [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> 2
{{1,2},{3,5},{4},{6}}
=> [2,1,5,4,3,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 3
{{1,2},{3},{4},{5,6}}
=> [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,3,4,6},{2,5}}
=> [3,5,4,6,2,1] => ([(2,3),(2,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 2
{{1,3,4,6},{2},{5}}
=> [3,2,4,6,5,1] => ([(1,5),(2,5),(5,3),(5,4)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> 2
{{1,3,4},{2},{5},{6}}
=> [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,3},{2,5},{4,6}}
=> [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
{{1,3},{2},{4,6},{5}}
=> [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 3
{{1,4,5,6},{2,3}}
=> [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> 2
{{1,4,5},{2,3,6}}
=> [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
{{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
{{1,5},{2,3},{4},{6}}
=> [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,6},{2,3},{4,5}}
=> [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 2
{{1,5,6},{2,4},{3}}
=> [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> 2
{{1,6},{2,4},{3,5}}
=> [6,4,5,2,3,1] => ([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],6)
=> 1
{{1},{2,4},{3,5},{6}}
=> [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
{{1},{2,4},{3},{5,6}}
=> [1,4,3,2,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 3
{{1,5},{2,6},{3,4}}
=> [5,6,4,3,1,2] => ([(2,5),(3,4)],6)
=> ([(2,5),(3,4)],6)
=> 1
{{1,6},{2,5},{3,4}}
=> [6,5,4,3,2,1] => ([],6)
=> ([],6)
=> 0
{{1,6},{2},{3,4},{5}}
=> [6,2,4,3,5,1] => ([(2,3),(2,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> 2
{{1},{2},{3,4,6},{5}}
=> [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,5},{2,6},{3},{4}}
=> [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> 1
{{1,6},{2,5},{3},{4}}
=> [6,5,3,4,2,1] => ([(4,5)],6)
=> ([(4,5)],6)
=> 1
{{1},{2,6},{3},{4,5}}
=> [1,6,3,5,4,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => ([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
{{1,2,3,7},{4},{5,6}}
=> [2,3,7,4,6,5,1] => ([(1,6),(5,3),(5,4),(6,2),(6,5)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 2
{{1,2,4,6,7},{3,5}}
=> [2,4,5,6,3,7,1] => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
=> 2
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St001645
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 41%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 41%
Values
{{1,2}}
=> [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1},{2}}
=> [1,2] => ([],2)
=> ([],1)
=> 1 = 0 + 1
{{1,2,3}}
=> [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,2},{3}}
=> [2,1,3] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,3} + 1
{{1,3},{2}}
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1},{2,3}}
=> [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,3} + 1
{{1},{2},{3}}
=> [1,2,3] => ([],3)
=> ([],1)
=> 1 = 0 + 1
{{1,2,3,4}}
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,2,4},{3}}
=> [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,2},{3,4}}
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,3,4},{2}}
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,3},{2,4}}
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,4},{2,3}}
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1},{2,3},{4}}
=> [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1},{2,4},{3}}
=> [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1},{2},{3,4}}
=> [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,2,2,2,3,3,4,4,5,6} + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => ([],4)
=> ([],1)
=> 1 = 0 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 4 + 1
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,8,8,9,10} + 1
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1 = 0 + 1
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16 = 15 + 1
{{1,3,5},{2,4,6}}
=> [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,6},{2,3,4,5}}
=> [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1,6},{2,3,5},{4}}
=> [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,4},{2,5},{3,6}}
=> [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,4},{2,6},{3,5}}
=> [4,6,5,1,3,2] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,5},{2,4},{3,6}}
=> [5,4,6,2,1,3] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,6},{2,4,5},{3}}
=> [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,6},{2,4},{3,5}}
=> [6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1,5},{2,6},{3,4}}
=> [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1,6},{2,5},{3,4}}
=> [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,5},{2,6},{3},{4}}
=> [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1,6},{2,5},{3},{4}}
=> [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 4 + 1
{{1,6},{2},{3},{4},{5}}
=> [6,2,3,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1 = 0 + 1
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1)],2)
=> 2 = 1 + 1
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16 = 15 + 1
{{1,2,4,6},{3,5,7}}
=> [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,2,4},{3,5,6,7}}
=> [2,4,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16 = 15 + 1
{{1,2,5},{3,6},{4,7}}
=> [2,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,3,5,7},{2,4,6}}
=> [3,4,5,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
{{1,3,5},{2,4,6,7}}
=> [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,3},{2,4,5,6,7}}
=> [3,4,1,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,3),(1,2),(2,3)],4)
=> 8 = 7 + 1
{{1,3},{2,4,6},{5,7}}
=> [3,4,1,6,7,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 16 = 15 + 1
{{1,7},{2,3,4,5,6}}
=> [7,3,4,5,6,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
{{1,7},{2,3,4,6},{5}}
=> [7,3,4,6,5,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
{{1,5},{2,3,7},{4,6}}
=> [5,3,7,6,1,4,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> 7 = 6 + 1
Description
The pebbling number of a connected graph.
Matching statistic: St001880
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 32%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 32%
Values
{{1,2}}
=> [2,1] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1}
{{1},{2}}
=> [1,2] => [2,1] => ([],2)
=> ? ∊ {0,1}
{{1,2,3}}
=> [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
{{1,2},{3}}
=> [2,1,3] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,2}
{{1,3},{2}}
=> [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,2}
{{1},{2,3}}
=> [1,3,2] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,2}
{{1},{2},{3}}
=> [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,2}
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,2,4},{3}}
=> [2,4,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
{{1,2},{3,4}}
=> [2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,3,4},{2}}
=> [3,2,4,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,3},{2,4}}
=> [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1},{2,3,4}}
=> [1,3,4,2] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1},{2,3},{4}}
=> [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1},{2,4},{3}}
=> [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1},{2},{3,4}}
=> [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1},{2},{3},{4}}
=> [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,3,5,6}
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,1,2,4,3] => ([(1,4),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
{{1,2,3,5,6},{4}}
=> [2,3,5,4,6,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 2
{{1,2,3,6},{4},{5}}
=> [2,3,6,4,5,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
{{1,2,4,5,6},{3}}
=> [2,4,3,5,6,1] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 4
{{1,2,5,6},{3,4}}
=> [2,5,4,3,6,1] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 2
{{1,2,6},{3,4,5}}
=> [2,6,4,5,3,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 1
{{1,2,6},{3,4},{5}}
=> [2,6,4,3,5,1] => [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
{{1,2,5,6},{3},{4}}
=> [2,5,3,4,6,1] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 5
{{1,2,6},{3,5},{4}}
=> [2,6,5,4,3,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
{{1,2,6},{3},{4,5}}
=> [2,6,3,5,4,1] => [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 2
{{1,2,6},{3},{4},{5}}
=> [2,6,3,4,5,1] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 4
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
{{1,2,3,4,5,7},{6}}
=> [2,3,4,5,7,6,1] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> 7
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7
{{1,2,3,4,7},{5,6}}
=> [2,3,4,7,6,5,1] => [1,2,3,6,5,4,7] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> 3
{{1,2,3,4,7},{5},{6}}
=> [2,3,4,7,5,6,1] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 6
{{1,2,3,5,6,7},{4}}
=> [2,3,5,4,6,7,1] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7
{{1,2,3,5,7},{4,6}}
=> [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 5
{{1,2,3,6,7},{4,5}}
=> [2,3,6,5,4,7,1] => [1,2,5,4,3,6,7] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> 3
{{1,2,3,7},{4,5,6}}
=> [2,3,7,5,6,4,1] => [1,2,6,4,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
=> 2
{{1,2,3,7},{4,5},{6}}
=> [2,3,7,5,4,6,1] => [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
=> 3
{{1,2,3,6,7},{4},{5}}
=> [2,3,6,4,5,7,1] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 6
{{1,2,3,7},{4,6},{5}}
=> [2,3,7,6,5,4,1] => [1,2,6,5,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> 2
{{1,2,3,7},{4},{5,6}}
=> [2,3,7,4,6,5,1] => [1,2,4,6,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
=> 3
{{1,2,3,7},{4},{5},{6}}
=> [2,3,7,4,5,6,1] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 5
{{1,2,4,5,6,7},{3}}
=> [2,4,3,5,6,7,1] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 7
{{1,2,4,5,7},{3,6}}
=> [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> 4
{{1,2,4,5,7},{3},{6}}
=> [2,4,3,5,7,6,1] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 7
{{1,2,4,6,7},{3,5}}
=> [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> 5
{{1,2,4,7},{3,5,6}}
=> [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
=> 2
{{1,2,4,7},{3,5},{6}}
=> [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> 6
{{1,2,4,7},{3,6},{5}}
=> [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
=> 2
{{1,2,5,6,7},{3,4}}
=> [2,5,4,3,6,7,1] => [1,4,3,2,5,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> 3
{{1,2,5,7},{3,4,6}}
=> [2,5,4,6,7,3,1] => [1,6,3,2,4,5,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> 2
{{1,2,6,7},{3,4,5}}
=> [2,6,4,5,3,7,1] => [1,5,3,4,2,6,7] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> 2
{{1,2,7},{3,4,5,6}}
=> [2,7,4,5,6,3,1] => [1,6,3,4,5,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> 1
{{1,2,7},{3,4,5},{6}}
=> [2,7,4,5,3,6,1] => [1,5,3,4,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> 2
{{1,2,6,7},{3,4},{5}}
=> [2,6,4,3,5,7,1] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> 3
{{1,2,7},{3,4,6},{5}}
=> [2,7,4,6,5,3,1] => [1,6,3,5,4,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001879
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 55%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 55%
Values
{{1,2}}
=> [2,1] => [2,1] => ([],2)
=> ? ∊ {0,1}
{{1},{2}}
=> [1,2] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1}
{{1,2,3}}
=> [2,3,1] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,3}
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,3}
{{1,3},{2}}
=> [3,2,1] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,3}
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,3}
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
{{1,2,3,4}}
=> [2,3,4,1] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,2,3},{4}}
=> [2,3,1,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,2,4},{3}}
=> [2,4,3,1] => [3,4,1,2] => ([(0,3),(1,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,3,4},{2}}
=> [3,2,4,1] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,3},{2,4}}
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,2,2,2,2,3,3,4,5,6}
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,1,2,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [4,1,3,5,2] => ([(0,4),(1,2),(1,3),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,5,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,1,5,2,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> ? ∊ {0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
{{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
{{1},{2,3,4},{5},{6}}
=> [1,3,4,2,5,6] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
{{1},{2,3,5},{4},{6}}
=> [1,3,5,4,2,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 8
{{1},{2,3},{4},{5},{6}}
=> [1,3,2,4,5,6] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
{{1},{2,4,5},{3},{6}}
=> [1,4,3,5,2,6] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
{{1},{2,4},{3,5},{6}}
=> [1,4,5,2,3,6] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
{{1},{2,4},{3},{5},{6}}
=> [1,4,3,2,5,6] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
{{1},{2,5},{3,4},{6}}
=> [1,5,4,3,2,6] => [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
{{1},{2},{3,4,5},{6}}
=> [1,2,4,5,3,6] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
{{1},{2},{3,4},{5},{6}}
=> [1,2,4,3,5,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
{{1},{2,5},{3},{4},{6}}
=> [1,5,3,4,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
{{1},{2},{3,5},{4},{6}}
=> [1,2,5,4,3,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
{{1},{2},{3},{4,5},{6}}
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
{{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
{{1},{2,3,4,5,6},{7}}
=> [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> 10
{{1},{2,3,4,5},{6},{7}}
=> [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> 9
{{1},{2,3,4,6},{5},{7}}
=> [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 10
{{1},{2,3,4},{5},{6},{7}}
=> [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 8
{{1},{2,3,5,6},{4},{7}}
=> [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> 9
{{1},{2,3,5},{4,6},{7}}
=> [1,3,5,6,2,4,7] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> 9
{{1},{2,3,5},{4},{6},{7}}
=> [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> 9
{{1},{2,3,6},{4,5},{7}}
=> [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> 13
{{1},{2,3,6},{4},{5},{7}}
=> [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 10
{{1},{2,3},{4},{5,6},{7}}
=> [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 8
{{1},{2,3},{4},{5},{6},{7}}
=> [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 7
{{1},{2,4,5,6},{3},{7}}
=> [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> 9
{{1},{2,4,5},{3,6},{7}}
=> [1,4,6,5,2,3,7] => [1,5,2,4,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
=> 11
{{1},{2,4,5},{3},{6},{7}}
=> [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 8
{{1},{2,4,6},{3,5},{7}}
=> [1,4,5,6,3,2,7] => [1,5,3,6,2,4,7] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 11
{{1},{2,4},{3,5},{6},{7}}
=> [1,4,5,2,3,6,7] => [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 8
{{1},{2,4,6},{3},{5},{7}}
=> [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> 9
{{1},{2,4},{3,6},{5},{7}}
=> [1,4,6,2,5,3,7] => [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> 9
{{1},{2,4},{3},{5},{6},{7}}
=> [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 8
{{1},{2,5},{3,4,6},{7}}
=> [1,5,4,6,2,3,7] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> 9
{{1},{2,5},{3,4},{6},{7}}
=> [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> 11
{{1},{2,6},{3,4,5},{7}}
=> [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> 13
{{1},{2},{3,4,5,6},{7}}
=> [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> 9
{{1},{2},{3,4,5},{6},{7}}
=> [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 8
{{1},{2,6},{3,4},{5},{7}}
=> [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> 12
{{1},{2},{3,4,6},{5},{7}}
=> [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)
=> 9
{{1},{2},{3,4},{5},{6},{7}}
=> [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7
{{1},{2,5,6},{3},{4},{7}}
=> [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> 9
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001232
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 32%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 32%
Values
{{1,2}}
=> [2] => [1,1,0,0]
=> [1,0,1,0]
=> 1
{{1},{2}}
=> [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 0
{{1,2,3}}
=> [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 3
{{1,2},{3}}
=> [2,1] => [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 1
{{1,3},{2}}
=> [2,1] => [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 1
{{1},{2,3}}
=> [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
{{1},{2},{3}}
=> [1,1,1] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
{{1,2,3,4}}
=> [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,2,3},{4}}
=> [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,2,4},{3}}
=> [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,2},{3,4}}
=> [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,2},{3},{4}}
=> [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 1
{{1,3,4},{2}}
=> [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,3},{2,4}}
=> [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1,3},{2},{4}}
=> [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 1
{{1,4},{2,3}}
=> [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1},{2,3,4}}
=> [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {2,2,3,3,4,4,5,6}
{{1},{2,3},{4}}
=> [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
{{1,4},{2},{3}}
=> [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 1
{{1},{2,4},{3}}
=> [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
{{1},{2},{3,4}}
=> [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
{{1},{2},{3},{4}}
=> [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
{{1,2,3,4,5}}
=> [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,4},{5}}
=> [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3,5},{4}}
=> [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4,5}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,3},{4},{5}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4,5},{3}}
=> [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3,5}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,4},{3},{5}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3,4}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4,5}}
=> [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,4},{5}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2,5},{3},{4}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3,5},{4}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4,5}}
=> [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,2},{3},{4},{5}}
=> [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,3,4,5},{2}}
=> [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2,5}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,4},{2},{5}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2,4}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4,5}}
=> [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,4},{5}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3,5},{2},{4}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2,5},{4}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4,5}}
=> [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,3},{2},{4},{5}}
=> [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,4,5},{2,3}}
=> [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3,5}}
=> [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,3},{5}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,3,4}}
=> [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4,5}}
=> [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,4},{5}}
=> [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,5},{2,3},{4}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3,5},{4}}
=> [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4,5}}
=> [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,3},{4},{5}}
=> [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
{{1,4,5},{2},{3}}
=> [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2,5},{3}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2},{3,5}}
=> [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1,4},{2},{3},{5}}
=> [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1,5},{2,4},{3}}
=> [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,4,5},{3}}
=> [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,4},{3,5}}
=> [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,4},{3},{5}}
=> [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
{{1,5},{2},{3,4}}
=> [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2,5},{3,4}}
=> [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2},{3,4,5}}
=> [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,8,8,9,10}
{{1},{2},{3,4},{5}}
=> [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
{{1,5},{2},{3},{4}}
=> [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
{{1},{2,5},{3},{4}}
=> [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
{{1},{2},{3,5},{4}}
=> [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
{{1},{2},{3},{4,5}}
=> [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
{{1},{2},{3},{4},{5}}
=> [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0
{{1,2},{3},{4},{5},{6}}
=> [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
{{1,3},{2},{4},{5},{6}}
=> [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
{{1},{2,3},{4},{5},{6}}
=> [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
{{1,4},{2},{3},{5},{6}}
=> [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
{{1},{2,4},{3},{5},{6}}
=> [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
{{1},{2},{3,4},{5},{6}}
=> [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
{{1,5},{2},{3},{4},{6}}
=> [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
{{1},{2,5},{3},{4},{6}}
=> [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
{{1},{2},{3,5},{4},{6}}
=> [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
{{1},{2},{3},{4,5},{6}}
=> [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
{{1,6},{2},{3},{4},{5}}
=> [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
{{1},{2,6},{3},{4},{5}}
=> [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
{{1},{2},{3,6},{4},{5}}
=> [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
{{1},{2},{3},{4,6},{5}}
=> [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
{{1},{2},{3},{4},{5,6}}
=> [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
{{1},{2},{3},{4},{5},{6}}
=> [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
{{1,2},{3},{4},{5},{6},{7}}
=> [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
{{1,3},{2},{4},{5},{6},{7}}
=> [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
{{1},{2,3},{4},{5},{6},{7}}
=> [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
{{1,4},{2},{3},{5},{6},{7}}
=> [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
{{1},{2,4},{3},{5},{6},{7}}
=> [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
{{1},{2},{3,4},{5},{6},{7}}
=> [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
{{1,5},{2},{3},{4},{6},{7}}
=> [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
{{1},{2,5},{3},{4},{6},{7}}
=> [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
{{1},{2},{3,5},{4},{6},{7}}
=> [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
{{1},{2},{3},{4,5},{6},{7}}
=> [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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