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Matching statistic: St000777
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
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] => [1] => ([],1)
=> 1
[-] => [1] => [1] => ([],1)
=> 1
[2,1] => [2,1] => [2,1] => ([(0,1)],2)
=> 2
[+,3,2] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[-,3,2] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> 3
[2,3,1] => [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
=> 3
[3,+,1] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[3,-,1] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 2
[+,+,4,3] => [1,2,4,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[-,+,4,3] => [1,2,4,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[+,-,4,3] => [1,2,4,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[-,-,4,3] => [1,2,4,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[+,3,4,2] => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[-,3,4,2] => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 4
[+,4,+,2] => [1,4,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-,4,+,2] => [1,4,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[+,4,-,2] => [1,4,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-,4,-,2] => [1,4,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,1,4,3] => [2,1,4,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,3,4,1] => [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,4,+,1] => [2,4,3,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,4,-,1] => [2,4,3,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[3,1,4,2] => [3,1,4,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 3
[3,+,4,1] => [3,2,4,1] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,-,4,1] => [3,2,4,1] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,4,2,1] => [3,4,2,1] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[4,1,+,2] => [4,1,3,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,1,-,2] => [4,1,3,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,+,1,3] => [4,2,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[4,-,1,3] => [4,2,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[4,+,+,1] => [4,2,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,-,+,1] => [4,2,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,+,-,1] => [4,2,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,-,-,1] => [4,2,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,+,+,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,+,+,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,-,+,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,-,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,-,+,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,+,-,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,-,-,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,-,-,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 5
[-,+,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 5
[+,-,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 5
[-,-,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 5
[+,+,5,+,3] => [1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,+,5,+,3] => [1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,5,+,3] => [1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001632
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 33%
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 33%
Values
[+] => [1] => [1] => ([],1)
=> ? = 1 - 1
[-] => [1] => [1] => ([],1)
=> ? = 1 - 1
[2,1] => [2,1] => [2,1] => ([(0,1)],2)
=> 1 = 2 - 1
[+,3,2] => [1,3,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-,3,2] => [1,3,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,3,1] => [2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,+,1] => [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[3,-,1] => [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 2 - 1
[+,+,4,3] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[-,+,4,3] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[+,-,4,3] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[-,-,4,3] => [1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[+,3,4,2] => [1,3,4,2] => [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
[-,3,4,2] => [1,3,4,2] => [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
[+,4,+,2] => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[-,4,+,2] => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[+,4,-,2] => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[-,4,-,2] => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
[2,1,4,3] => [2,1,4,3] => [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
[2,3,4,1] => [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
[2,4,+,1] => [2,4,3,1] => [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
[2,4,-,1] => [2,4,3,1] => [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
[3,1,4,2] => [3,1,4,2] => [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,+,4,1] => [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
[3,-,4,1] => [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
[3,4,2,1] => [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
[4,1,+,2] => [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
[4,1,-,2] => [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
[4,+,1,3] => [4,2,1,3] => [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
[4,-,1,3] => [4,2,1,3] => [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
[4,+,+,1] => [4,2,3,1] => [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
[4,-,+,1] => [4,2,3,1] => [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
[4,+,-,1] => [4,2,3,1] => [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
[4,-,-,1] => [4,2,3,1] => [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
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 2 - 1
[+,+,+,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[-,+,+,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[+,-,+,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[+,+,-,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[-,-,+,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[-,+,-,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[+,-,-,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[-,-,-,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 - 1
[+,+,4,5,3] => [1,2,4,5,3] => [4,1,2,5,3] => ([(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
[-,+,4,5,3] => [1,2,4,5,3] => [4,1,2,5,3] => ([(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
[+,-,4,5,3] => [1,2,4,5,3] => [4,1,2,5,3] => ([(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
[-,-,4,5,3] => [1,2,4,5,3] => [4,1,2,5,3] => ([(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
[+,+,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[-,+,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[+,-,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[+,+,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[-,-,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[-,+,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[+,-,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[-,-,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 3 - 1
[+,3,2,5,4] => [1,3,2,5,4] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 5 - 1
[-,3,2,5,4] => [1,3,2,5,4] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 5 - 1
[+,3,4,5,2] => [1,3,4,5,2] => [3,1,4,5,2] => ([(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
[-,3,4,5,2] => [1,3,4,5,2] => [3,1,4,5,2] => ([(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
[+,3,5,+,2] => [1,3,5,4,2] => [5,3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 5 - 1
[-,3,5,+,2] => [1,3,5,4,2] => [5,3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 5 - 1
[+,3,5,-,2] => [1,3,5,4,2] => [5,3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 5 - 1
[-,3,5,-,2] => [1,3,5,4,2] => [5,3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 5 - 1
[+,4,2,5,3] => [1,4,2,5,3] => [4,5,1,2,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 4 - 1
[-,4,2,5,3] => [1,4,2,5,3] => [4,5,1,2,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 4 - 1
[+,4,+,5,2] => [1,4,3,5,2] => [4,3,1,5,2] => ([(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
[-,4,+,5,2] => [1,4,3,5,2] => [4,3,1,5,2] => ([(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
[+,4,-,5,2] => [1,4,3,5,2] => [4,3,1,5,2] => ([(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
[5,4,+,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[5,4,-,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 2 - 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 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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