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Your data matches 31 different statistics following compositions of up to 3 maps.
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Matching statistic: St000266
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Mp00160: Permutations —graph of inversions⟶ Graphs
St000266: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000266: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
=> 1
[1,2] => ([],2)
=> 1
[2,1] => ([(0,1)],2)
=> 1
[1,2,3] => ([],3)
=> 1
[1,3,2] => ([(1,2)],3)
=> 1
[2,1,3] => ([(1,2)],3)
=> 1
[2,3,1] => ([(0,2),(1,2)],3)
=> 1
[3,1,2] => ([(0,2),(1,2)],3)
=> 1
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 4
[1,2,3,4] => ([],4)
=> 1
[1,2,4,3] => ([(2,3)],4)
=> 1
[1,3,2,4] => ([(2,3)],4)
=> 1
[1,3,4,2] => ([(1,3),(2,3)],4)
=> 1
[1,4,2,3] => ([(1,3),(2,3)],4)
=> 1
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 4
[2,1,3,4] => ([(2,3)],4)
=> 1
[2,1,4,3] => ([(0,3),(1,2)],4)
=> 1
[2,3,1,4] => ([(1,3),(2,3)],4)
=> 1
[2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 1
[2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,1,2,4] => ([(1,3),(2,3)],4)
=> 1
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 1
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 4
[3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 5
[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 14
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 14
[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 14
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 38
[1,2,3,4,5] => ([],5)
=> 1
[1,2,3,5,4] => ([(3,4)],5)
=> 1
[1,2,4,3,5] => ([(3,4)],5)
=> 1
[1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 1
[1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 1
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> 4
[1,3,2,4,5] => ([(3,4)],5)
=> 1
[1,3,2,5,4] => ([(1,4),(2,3)],5)
=> 1
[1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 1
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 1
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[1,4,2,3,5] => ([(2,4),(3,4)],5)
=> 1
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 1
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 4
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 5
Description
The number of spanning subgraphs of a graph with the same connected components.
A subgraph or factor of a graph is spanning, if it has the same vertex set [1]. The present statistic additionally requires the subgraph to have the same components. It can be obtained by evaluating the Tutte polynomial at the points $x=1$ and $y=2$, see [2,3].
By mistake, [2] refers to this statistic as the number of spanning subgraphs, which would be $2^m$, where $m$ is the number of edges. Equivalently, this would be the evaluation of the Tutte polynomial at $x=y=2$.
Matching statistic: St001563
Mp00065: Permutations —permutation poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St001563: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 15%●distinct values known / distinct values provided: 3%
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St001563: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 15%●distinct values known / distinct values provided: 3%
Values
[1] => ([],1)
=> [1]
=> 1
[1,2] => ([(0,1)],2)
=> [1]
=> 1
[2,1] => ([],2)
=> [2]
=> 1
[1,2,3] => ([(0,2),(2,1)],3)
=> [1]
=> 1
[1,3,2] => ([(0,1),(0,2)],3)
=> [2]
=> 1
[2,1,3] => ([(0,2),(1,2)],3)
=> [2]
=> 1
[2,3,1] => ([(1,2)],3)
=> [3]
=> 1
[3,1,2] => ([(1,2)],3)
=> [3]
=> 1
[3,2,1] => ([],3)
=> [3,3]
=> 4
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> [1]
=> 1
[1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> [2]
=> 1
[1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> 1
[1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> [3]
=> 1
[1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> [3]
=> 1
[1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> 4
[2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> [2]
=> 1
[2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> 4
[2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> [3]
=> 1
[2,3,4,1] => ([(1,2),(2,3)],4)
=> [4]
=> 1
[2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 4
[2,4,3,1] => ([(1,2),(1,3)],4)
=> [8]
=> ? ∊ {1,1,1,5,14,14,14,38}
[3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> [3]
=> 1
[3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 4
[3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> 4
[3,2,4,1] => ([(1,3),(2,3)],4)
=> [8]
=> ? ∊ {1,1,1,5,14,14,14,38}
[3,4,1,2] => ([(0,3),(1,2)],4)
=> [4,2]
=> 4
[3,4,2,1] => ([(2,3)],4)
=> [4,4,4]
=> ? ∊ {1,1,1,5,14,14,14,38}
[4,1,2,3] => ([(1,2),(2,3)],4)
=> [4]
=> 1
[4,1,3,2] => ([(1,2),(1,3)],4)
=> [8]
=> ? ∊ {1,1,1,5,14,14,14,38}
[4,2,1,3] => ([(1,3),(2,3)],4)
=> [8]
=> ? ∊ {1,1,1,5,14,14,14,38}
[4,2,3,1] => ([(2,3)],4)
=> [4,4,4]
=> ? ∊ {1,1,1,5,14,14,14,38}
[4,3,1,2] => ([(2,3)],4)
=> [4,4,4]
=> ? ∊ {1,1,1,5,14,14,14,38}
[4,3,2,1] => ([],4)
=> [4,4,4,4,4,4]
=> ? ∊ {1,1,1,5,14,14,14,38}
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> 1
[1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> 1
[1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> [2]
=> 1
[1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> 1
[1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> 1
[1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> 4
[1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> 1
[1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> 4
[1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> 1
[1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 1
[1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 4
[1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> 1
[1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 4
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> 4
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> 4
[1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 1
[1,5,2,4,3] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,2,3] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> [4,4,4,4,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> 1
[2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> 4
[2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> 4
[2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 1
[2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 1
[2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> 1
[2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> 1
[2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> [4]
=> 1
[2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> [5]
=> 1
[2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
=> [15]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,1,4,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,1,4] => ([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
=> [15]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,2,5,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
=> [15]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,4,5,2,1] => ([(2,3),(3,4)],5)
=> [5,5,5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,2,1,4] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[3,5,4,2,1] => ([(2,3),(2,4)],5)
=> [10,10,10,10]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[4,1,3,2,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[4,1,3,5,2] => ([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[4,1,5,2,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
Description
The value of the power-sum symmetric function evaluated at 1.
The statistic is $p_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=x_2=\dotsb=x_k$,
where $\lambda$ has $k$ parts.
Matching statistic: St001964
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00223: Permutations —runsort⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 13%●distinct values known / distinct values provided: 2%
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 13%●distinct values known / distinct values provided: 2%
Values
[1] => [1] => [1] => ([],1)
=> 0 = 1 - 1
[1,2] => [1,2] => [2,1] => ([],2)
=> 0 = 1 - 1
[2,1] => [1,2] => [2,1] => ([],2)
=> 0 = 1 - 1
[1,2,3] => [1,2,3] => [3,2,1] => ([],3)
=> 0 = 1 - 1
[1,3,2] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {1,4} - 1
[2,1,3] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {1,4} - 1
[2,3,1] => [1,2,3] => [3,2,1] => ([],3)
=> 0 = 1 - 1
[3,1,2] => [1,2,3] => [3,2,1] => ([],3)
=> 0 = 1 - 1
[3,2,1] => [1,2,3] => [3,2,1] => ([],3)
=> 0 = 1 - 1
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[1,3,4,2] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,4,2,3] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[1,4,3,2] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[2,1,3,4] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> 0 = 1 - 1
[2,1,4,3] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[2,3,1,4] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[2,3,4,1] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[2,4,1,3] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[2,4,3,1] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[3,1,2,4] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[3,1,4,2] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[3,2,1,4] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[3,2,4,1] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[3,4,1,2] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[3,4,2,1] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[4,1,2,3] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[4,1,3,2] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[4,2,1,3] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {1,1,1,4,4,4,4,4,4,5,14,14,14,38} - 1
[4,2,3,1] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[4,3,1,2] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[4,3,2,1] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[1,2,3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,2,4,3,5] => [1,2,4,3,5] => [5,4,2,3,1] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,2,4,5,3] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,2,5,3,4] => [1,2,5,3,4] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,2,5,4,3] => [1,2,5,3,4] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,3,2,4,5] => [1,3,2,4,5] => [5,3,4,2,1] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,3,2,5,4] => [1,3,2,5,4] => [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,3,4,2,5] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,3,4,5,2] => [1,3,4,5,2] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,3,5,2,4] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,3,5,4,2] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,2,3,5] => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,2,5,3] => [1,4,2,5,3] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,3,2,5] => [1,4,2,5,3] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,3,5,2] => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,5,2,3] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,4,5,3,2] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,2,3,4] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,2,4,3] => [1,5,2,4,3] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,3,2,4] => [1,5,2,4,3] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,3,4,2] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,4,2,3] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[1,5,4,3,2] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,3,4,5] => [1,3,4,5,2] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,3,5,4] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,4,3,5] => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,4,5,3] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,5,3,4] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,1,5,4,3] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,3,1,4,5] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,3,1,5,4] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,3,4,1,5] => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,3,4,5,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[2,3,5,1,4] => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,3,5,4,1] => [1,2,3,5,4] => [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,4,1,3,5] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,4,1,5,3] => [1,5,2,4,3] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} - 1
[2,4,5,3,1] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[2,5,1,3,4] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,1,2,4,5] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,2,4,5,1] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[3,4,5,1,2] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[3,4,5,2,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[4,5,1,2,3] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[4,5,2,3,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[4,5,3,1,2] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[4,5,3,2,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,1,2,3,4] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,1,3,4,2] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[5,2,1,3,4] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[5,2,3,4,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,3,4,1,2] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,3,4,2,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,4,1,2,3] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,4,2,3,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,4,3,1,2] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[5,4,3,2,1] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => ([],6)
=> 0 = 1 - 1
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,2,4,5,3,6] => [1,2,4,5,3,6] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6)
=> 0 = 1 - 1
[1,3,4,2,5,6] => [1,3,4,2,5,6] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6)
=> 0 = 1 - 1
[1,3,5,2,6,4] => [1,3,5,2,6,4] => [6,4,2,5,1,3] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> 0 = 1 - 1
[1,3,5,4,2,6] => [1,3,5,2,6,4] => [6,4,2,5,1,3] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> 0 = 1 - 1
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => ([],6)
=> 0 = 1 - 1
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St001630
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
[1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[4,1,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,5,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,5,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,5,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,3,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,4,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
[1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 1
[3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 1
[4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 1
[2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[4,1,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,2,5,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,3,5,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,4,5,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,2,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,3,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,5,4,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001876
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
[1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1
[1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,5,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,5,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,3,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,4,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001877
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
[1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1
[1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4}
[3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,2,5,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,5,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,4,5,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,2,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,3,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,4,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001875
Values
[1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 2
[1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 2
[2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 2
[2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 2
[3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,4} + 2
[3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[4,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38} + 2
[4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,4,5,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728} + 2
[5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,2,5,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,3,5,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,3,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,4,5,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,2,4,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,3,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,4,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St000771
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 7%●distinct values known / distinct values provided: 2%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 7%●distinct values known / distinct values provided: 2%
Values
[1] => [1] => ([],1)
=> ([],1)
=> 1
[1,2] => [1,2] => ([],2)
=> ([],1)
=> 1
[2,1] => [1,2] => ([],2)
=> ([],1)
=> 1
[1,2,3] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[1,3,2] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[2,1,3] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[2,3,1] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,4}
[3,2,1] => [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,4}
[1,2,3,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,2,4,3] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,3,2,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,3,4,2] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,3,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,1,4,3] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,3,1,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,3,4,1] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$
\left(\begin{array}{rrrr}
4 & -1 & -2 & -1 \\
-1 & 4 & -1 & -2 \\
-2 & -1 & 4 & -1 \\
-1 & -2 & -1 & 4
\end{array}\right).
$$
Its eigenvalues are $0,4,4,6$, so the statistic is $2$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Matching statistic: St000772
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 7%●distinct values known / distinct values provided: 2%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 7%●distinct values known / distinct values provided: 2%
Values
[1] => [1] => ([],1)
=> ([],1)
=> 1
[1,2] => [1,2] => ([],2)
=> ([],1)
=> 1
[2,1] => [1,2] => ([],2)
=> ([],1)
=> 1
[1,2,3] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[1,3,2] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[2,1,3] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[2,3,1] => [1,2,3] => ([],3)
=> ([],1)
=> 1
[3,1,2] => [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,4}
[3,2,1] => [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {1,4}
[1,2,3,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,2,4,3] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,3,2,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,3,4,2] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[1,4,2,3] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,4,3,2] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,1,3,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,1,4,3] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,3,1,4] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,3,4,1] => [1,2,3,4] => ([],4)
=> ([],1)
=> 1
[2,4,1,3] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,1,4] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,1,2] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[3,4,2,1] => [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,14,14,14,38}
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,3,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,4,3,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,4,5,3] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,2,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,2,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,4,2,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,4,5,2] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,3,5,4,2] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,2,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,2,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,3,5,2] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,2,3] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,4,5,3,2] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,2,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,2,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,3,4,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,2,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,5,4,3,2] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,3,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,3,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,4,3,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,4,5,3] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,1,5,4,3] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,1,4,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,1,5,4] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,4,1,5] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,4,5,1] => [1,2,3,4,5] => ([],5)
=> ([],1)
=> 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,1,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,1,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,1,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,3,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,1,3] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,4,5,3,1] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,1,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,1,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,1,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,1,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,16,16,18,18,19,19,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,124,124,124,124,124,124,134,134,134,314,314,314,314,728}
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,5,2,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[1,3,4,5,6,2] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,4,6,5] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
[2,1,3,5,4,6] => [1,2,3,4,5,6] => ([],6)
=> ([],1)
=> 1
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$
\left(\begin{array}{rrrr}
4 & -1 & -2 & -1 \\
-1 & 4 & -1 & -2 \\
-2 & -1 & 4 & -1 \\
-1 & -2 & -1 & 4
\end{array}\right).
$$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
The following 21 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St001330The hat guessing number of a graph. St000635The number of strictly order preserving maps of a poset into itself. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000914The sum of the values of the Möbius function of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000264The girth of a graph, which is not a tree. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type.
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