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Matching statistic: St001630
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[2,4,1,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,2,4] => [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,3,4,5,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,3,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,4,5,1,3] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,5,3,1,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,5,4,1,3] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,1,4,5,2] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[3,2,4,5,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[3,5,1,2,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,5,2,1,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,1,2,5,3] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[4,1,3,5,2] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[5,1,2,3,4] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[5,1,2,4,3] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[1,2,4,6,3,5] => [1,2,5,6,3,4] => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,4,5,6,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,5,6,2,4] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,6,4,2,5] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,6,5,2,4] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,4,2,5,6,3] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,4,3,5,6,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,4,6,2,3,5] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,4,6,3,2,5] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,5,2,3,6,4] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,5,2,4,6,3] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,6,2,3,4,5] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,6,2,3,5,4] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,3,6,5] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[2,1,4,6,3,5] => [2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[2,3,4,5,1,6] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1
[2,3,4,5,6,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[2,3,5,6,1,4] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[2,3,6,4,1,5] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[2,3,6,5,1,4] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[2,4,1,3,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,4,1,3,6,5] => [3,4,1,2,6,5] => ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[2,4,1,6,3,5] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 2
[2,4,5,1,3,6] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,4,5,1,6,3] => [4,6,3,1,5,2] => ([(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[2,4,6,3,5,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,4,6,5,1,3] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,5,3,1,4,6] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,5,3,1,6,4] => [4,6,3,1,5,2] => ([(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[2,5,4,1,3,6] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St000455
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => [3] => ([],3)
=> ? = 1 - 2
[1,2,3,4] => [1,2,3,4] => [4] => ([],4)
=> ? = 2 - 2
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[1,2,3,4,5] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 - 2
[1,3,5,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[2,3,4,5,1] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[2,4,1,3,5] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[2,4,5,1,3] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
[2,5,3,1,4] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
[2,5,4,1,3] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
[3,1,4,5,2] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[3,2,4,5,1] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[3,5,1,2,4] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
[3,5,2,1,4] => [4,5,3,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0 = 2 - 2
[4,1,2,5,3] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[4,1,3,5,2] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[5,1,2,3,4] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[5,1,2,4,3] => [5,2,3,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 - 2
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [6] => ([],6)
=> ? = 1 - 2
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [2,4] => ([(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 2
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 2
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,4,6,7,3,5] => [1,2,6,7,5,3,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,4,7,5,3,6] => [1,2,6,7,5,3,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,4,7,6,3,5] => [1,2,6,7,5,3,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,5,7,3,4,6] => [1,2,6,7,5,3,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,2,5,7,4,3,6] => [1,2,6,7,5,3,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,3,5,2,4,6,7] => [1,4,5,2,3,6,7] => [3,4] => ([(3,6),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,3,5,6,2,4,7] => [1,5,6,4,2,3,7] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,3,5,7,6,2,4] => [1,6,7,5,4,2,3] => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,3,6,4,2,5,7] => [1,5,6,4,2,3,7] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
[1,3,6,5,2,4,7] => [1,5,6,4,2,3,7] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0 = 2 - 2
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Matching statistic: St001645
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
=> ? = 1 + 5
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? = 2 + 5
[2,4,1,3] => [3,4,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? = 2 + 5
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> ? = 1 + 5
[1,3,5,2,4] => [1,4,5,2,3] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 2 + 5
[2,3,4,5,1] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[2,4,1,3,5] => [3,4,1,2,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 5
[2,4,5,1,3] => [4,5,3,1,2] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 5
[2,5,3,1,4] => [4,5,3,1,2] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 5
[2,5,4,1,3] => [4,5,3,1,2] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 5
[3,1,4,5,2] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[3,2,4,5,1] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[3,5,1,2,4] => [4,5,3,1,2] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 5
[3,5,2,1,4] => [4,5,3,1,2] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2 + 5
[4,1,2,5,3] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[4,1,3,5,2] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[5,1,2,3,4] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[5,1,2,4,3] => [5,2,3,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 5
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6)
=> ? = 1 + 5
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? = 2 + 5
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 5
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [4,3,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 5
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [3,2,1,6,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ? = 2 + 5
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,1,2,4,3,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 5
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [6,1,2,3,5,4] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [1,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [1,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [1,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [2,5,3,4,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [4,1,3,6,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [1,5,4,2,3,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [5,6,1,3,4,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 2 + 5
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [1,6,5,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [1,5,4,2,3,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [5,6,1,3,4,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? = 2 + 5
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [1,5,4,2,3,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 + 5
[1,3,5,6,2,7,4] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,3,6,4,2,7,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,3,6,5,2,7,4] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,3,7,4,2,5,6] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,3,7,4,2,6,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,6,2,3,7,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,6,3,2,7,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,7,2,3,5,6] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,7,2,3,6,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,7,3,2,5,6] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[1,4,7,3,2,6,5] => [1,5,7,4,2,6,3] => [4,6,7,1,3,5,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 2 + 5
[2,3,5,6,1,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[2,3,6,4,1,7,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[2,3,6,5,1,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[2,3,7,4,1,5,6] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[2,3,7,4,1,6,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[2,4,6,5,1,7,3] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,5,6,3,1,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,5,6,4,1,7,3] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,6,4,3,1,7,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,6,4,5,1,7,3] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,6,5,3,1,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,6,5,4,1,7,3] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,7,4,3,1,5,6] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[2,7,4,3,1,6,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,1,5,6,2,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,1,6,4,2,7,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,1,6,5,2,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,1,7,4,2,5,6] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,1,7,4,2,6,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,2,5,6,1,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,2,6,4,1,7,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,2,6,5,1,7,4] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,2,7,4,1,5,6] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,2,7,4,1,6,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[3,5,6,1,2,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,5,6,2,1,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,6,4,1,2,7,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,6,4,2,1,7,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,6,5,1,2,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,6,5,2,1,7,4] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,7,4,1,2,5,6] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,7,4,1,2,6,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,7,4,2,1,5,6] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[3,7,4,2,1,6,5] => [5,7,4,3,1,6,2] => [6,7,4,1,3,5,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 7 = 2 + 5
[4,1,6,2,3,7,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[4,1,6,3,2,7,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[4,1,7,2,3,5,6] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[4,1,7,2,3,6,5] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
[4,1,7,3,2,5,6] => [5,2,7,4,1,6,3] => [6,4,7,1,3,5,2] => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> 7 = 2 + 5
Description
The pebbling number of a connected graph.
Matching statistic: St001632
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? = 1 - 2
[1,2,3,4] => [1,4,3,2] => [4,3,1,2] => ([(2,3)],4)
=> ? = 2 - 2
[2,4,1,3] => [2,4,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? = 2 - 2
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,1,2] => ([(3,4)],5)
=> ? = 1 - 2
[1,3,5,2,4] => [1,5,4,3,2] => [5,4,3,1,2] => ([(3,4)],5)
=> ? = 2 - 2
[2,3,4,5,1] => [2,5,4,3,1] => [5,4,2,3,1] => ([(3,4)],5)
=> ? = 1 - 2
[2,4,1,3,5] => [2,5,1,4,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 2 - 2
[2,4,5,1,3] => [2,5,4,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> ? = 2 - 2
[2,5,3,1,4] => [2,5,4,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> ? = 2 - 2
[2,5,4,1,3] => [2,5,4,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> ? = 2 - 2
[3,1,4,5,2] => [3,1,5,4,2] => [5,1,3,4,2] => ([(1,3),(1,4),(4,2)],5)
=> ? = 1 - 2
[3,2,4,5,1] => [3,2,5,4,1] => [3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5)
=> ? = 1 - 2
[3,5,1,2,4] => [3,5,1,4,2] => [3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5)
=> 0 = 2 - 2
[3,5,2,1,4] => [3,5,2,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 2
[4,1,2,5,3] => [4,1,5,3,2] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
=> ? = 1 - 2
[4,1,3,5,2] => [4,1,5,3,2] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
=> ? = 1 - 2
[5,1,2,3,4] => [5,1,4,3,2] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> ? = 1 - 2
[5,1,2,4,3] => [5,1,4,3,2] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> ? = 1 - 2
[1,2,3,4,5,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,2,4,6,3,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,3,4,5,6,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,3,5,2,4,6] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,3,5,6,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,3,6,4,2,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,3,6,5,2,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,4,2,5,6,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,4,3,5,6,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,4,6,2,3,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,4,6,3,2,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 2 - 2
[1,5,2,3,6,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,5,2,4,6,3] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,6,2,3,4,5] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[1,6,2,3,5,4] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(4,5)],6)
=> ? = 1 - 2
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6)
=> ? = 1 - 2
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6)
=> ? = 2 - 2
[2,3,4,5,1,6] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 1 - 2
[2,3,4,5,6,1] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => ([(4,5)],6)
=> ? = 2 - 2
[2,3,5,6,1,4] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,6,4,1,5] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,3,6,5,1,4] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,4,1,3,5,6] => [2,6,1,5,4,3] => [6,2,5,4,1,3] => ([(1,5),(2,3),(2,4),(2,5)],6)
=> ? = 2 - 2
[2,4,1,3,6,5] => [2,6,1,5,4,3] => [6,2,5,4,1,3] => ([(1,5),(2,3),(2,4),(2,5)],6)
=> ? = 2 - 2
[2,4,1,6,3,5] => [2,6,1,5,4,3] => [6,2,5,4,1,3] => ([(1,5),(2,3),(2,4),(2,5)],6)
=> ? = 2 - 2
[2,4,5,1,3,6] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,4,5,1,6,3] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,4,6,3,5,1] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => ([(4,5)],6)
=> ? = 2 - 2
[2,4,6,5,1,3] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,5,3,1,4,6] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,5,3,1,6,4] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,5,4,1,3,6] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,5,4,1,6,3] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,5,6,3,1,4] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,5,6,4,1,3] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,3,1,4,5] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,6,3,1,5,4] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[2,6,4,3,1,5] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,4,5,1,3] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,5,3,1,4] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[2,6,5,4,1,3] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6)
=> ? = 2 - 2
[3,1,4,5,2,6] => [3,1,6,5,4,2] => [6,5,1,3,4,2] => ([(2,3),(2,4),(4,5)],6)
=> ? = 1 - 2
[3,4,6,1,5,2] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
=> 0 = 2 - 2
[3,5,2,1,4,6] => [3,6,2,1,5,4] => [3,2,6,5,1,4] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[3,5,2,1,6,4] => [3,6,2,1,5,4] => [3,2,6,5,1,4] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[3,5,6,1,2,4] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
=> 0 = 2 - 2
[3,6,2,1,4,5] => [3,6,2,1,5,4] => [3,2,6,5,1,4] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [3,2,6,5,1,4] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[3,6,4,1,2,5] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
=> 0 = 2 - 2
[3,6,5,1,2,4] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
=> 0 = 2 - 2
[4,2,6,1,5,3] => [4,2,6,1,5,3] => [2,4,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)
=> 0 = 2 - 2
[4,3,6,1,5,2] => [4,3,6,1,5,2] => [4,3,6,1,5,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> 0 = 2 - 2
[4,6,2,1,3,5] => [4,6,2,1,5,3] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[4,6,2,3,1,5] => [4,6,2,5,1,3] => [4,6,2,1,5,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> 0 = 2 - 2
[4,6,3,1,2,5] => [4,6,3,1,5,2] => [1,6,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> 0 = 2 - 2
[5,2,6,1,3,4] => [5,2,6,1,4,3] => [5,2,6,1,4,3] => ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[5,2,6,1,4,3] => [5,2,6,1,4,3] => [5,2,6,1,4,3] => ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> 0 = 2 - 2
[6,2,4,1,3,5] => [6,2,5,1,4,3] => [2,6,5,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[6,2,4,1,5,3] => [6,2,5,1,4,3] => [2,6,5,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[6,2,5,1,3,4] => [6,2,5,1,4,3] => [2,6,5,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
[6,2,5,1,4,3] => [6,2,5,1,4,3] => [2,6,5,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> 0 = 2 - 2
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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