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Matching statistic: St000777
Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1] => ([],1)
=> 1
[2,1] => [1] => ([],1)
=> 1
[2,1,3] => [2,1] => ([(0,1)],2)
=> 2
[2,3,1] => [2,1] => ([(0,1)],2)
=> 2
[3,2,1] => [2,1] => ([(0,1)],2)
=> 2
[2,3,1,4] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[2,3,4,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[2,4,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[3,1,2,4] => [3,1,2] => ([(0,2),(1,2)],3)
=> 3
[3,1,4,2] => [3,1,2] => ([(0,2),(1,2)],3)
=> 3
[3,2,1,4] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[3,2,4,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[3,4,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
=> 3
[3,4,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[4,2,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[4,3,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
=> 3
[4,3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[2,3,4,1,5] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,3,4,5,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,3,5,4,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,4,1,3,5] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[2,4,1,5,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[2,4,3,1,5] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,4,3,5,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,4,5,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[2,4,5,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,5,3,4,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,5,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[2,5,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,1,4,2,5] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[3,1,4,5,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[3,1,5,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[3,2,4,1,5] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,2,4,5,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,2,5,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,4,1,2,5] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3
[3,4,1,5,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3
[3,4,2,1,5] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[3,4,2,5,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[3,4,5,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3
[3,4,5,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[3,5,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[3,5,2,4,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,5,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3
[3,5,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[4,1,2,3,5] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 3
[4,1,2,5,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 3
[4,1,3,2,5] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,1,3,5,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,1,5,2,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001632
Mp00252: Permutations —restriction⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 29%
Mp00209: Permutations —pattern poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 29%
Values
[1,2] => [1] => ([],1)
=> ? = 1 - 1
[2,1] => [1] => ([],1)
=> ? = 1 - 1
[2,1,3] => [2,1] => ([(0,1)],2)
=> 1 = 2 - 1
[2,3,1] => [2,1] => ([(0,1)],2)
=> 1 = 2 - 1
[3,2,1] => [2,1] => ([(0,1)],2)
=> 1 = 2 - 1
[2,3,1,4] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,3,4,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,1,2,4] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,1,4,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,2,1,4] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[3,2,4,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[3,4,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[4,2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[2,3,4,1,5] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,3,4,5,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,3,5,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,4,1,3,5] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[2,4,1,5,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[2,4,3,1,5] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[2,4,3,5,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[2,4,5,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[2,4,5,3,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[2,5,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,5,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[2,5,4,3,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[3,1,4,2,5] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[3,1,4,5,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[3,1,5,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[3,2,4,1,5] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[3,2,4,5,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[3,2,5,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[3,4,1,2,5] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
[3,4,1,5,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
[3,4,2,1,5] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,4,2,5,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,4,5,1,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
[3,4,5,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[3,5,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[3,5,2,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[3,5,4,1,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
[3,5,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,3,5] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,2,5,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,3,2,5] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,1,3,5,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,1,5,2,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,1,5,3,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,2,1,3,5] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,2,1,5,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,2,3,1,5] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 3 - 1
[4,2,3,5,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 3 - 1
[4,2,5,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,2,5,3,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 3 - 1
[4,3,1,2,5] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,1,5,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,2,1,5] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[4,3,2,5,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[4,3,5,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,3,5,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[4,5,1,2,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,5,1,3,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,5,2,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[4,5,2,3,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 3 - 1
[4,5,3,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[4,5,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[5,2,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[5,2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[5,2,4,3,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[5,3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 4 - 1
[5,3,2,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[5,3,4,1,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
[5,3,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[5,4,1,2,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[5,4,1,3,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[5,4,2,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 4 - 1
[5,4,2,3,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 3 - 1
[5,4,3,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[5,4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[2,3,4,5,1,6] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[2,3,4,5,6,1] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[2,3,4,6,5,1] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[2,3,5,1,4,6] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 5 - 1
[2,3,5,1,6,4] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 5 - 1
[2,3,5,4,1,6] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 - 1
[2,3,5,4,6,1] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 - 1
[2,3,5,6,1,4] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 5 - 1
[2,3,5,6,4,1] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 - 1
[2,3,6,4,5,1] => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[2,3,6,5,1,4] => [2,3,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 5 - 1
[2,3,6,5,4,1] => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 - 1
[2,4,1,5,3,6] => [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? = 5 - 1
[5,4,3,2,1,6] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[5,4,3,2,6,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[5,4,3,6,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[5,4,6,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[5,6,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
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