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Your data matches 10 different statistics following compositions of up to 3 maps.
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Matching statistic: St001880
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Mp00277: Permutations —catalanization⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [5,3,2,4,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[3,5,2,4,1] => [5,4,2,3,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[4,2,5,1,3] => [5,2,4,3,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[4,3,5,1,2] => [5,3,4,2,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[4,5,1,3,2] => [5,3,4,2,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[4,5,2,3,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [5,4,2,3,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,3,4,1,2] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 4
[3,6,2,5,4,1] => [6,4,2,5,3,1] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[3,6,4,2,5,1] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[4,2,6,1,5,3] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 1
[4,3,6,1,5,2] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 2
[4,3,6,2,5,1] => [6,3,5,2,4,1] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[4,5,1,6,2,3] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 2
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[4,6,1,5,3,2] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 2
[4,6,2,5,3,1] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[4,6,3,5,2,1] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[4,6,5,1,2,3] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,2,6,1,4,3] => [6,2,4,5,3,1] => [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 2
[5,3,2,6,1,4] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 4
[5,3,6,1,4,2] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 2
[5,3,6,2,4,1] => [6,3,5,4,2,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[5,4,2,6,1,3] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 2
[5,4,3,6,1,2] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,4,6,2,3,1] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[5,4,6,3,1,2] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[5,6,1,4,3,2] => [6,3,5,4,2,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[5,6,2,4,3,1] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [6,4,2,5,3,1] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[6,2,5,3,1,4] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[6,3,2,5,1,4] => [6,3,5,2,4,1] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[6,3,5,1,4,2] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[6,3,5,2,4,1] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[6,4,2,5,1,3] => [6,3,5,4,2,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[6,4,3,5,1,2] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[6,4,5,1,3,2] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001330
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(load all 7 compositions to match this statistic)
Mp00277: Permutations —catalanization⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 71%
Mp00160: Permutations —graph of inversions⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,5,1,4,2] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4
[3,5,2,4,1] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5
[4,2,5,1,3] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4
[4,3,5,1,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5
[4,5,1,3,2] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5
[4,5,2,3,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,5,3,1,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,2,4,1,3] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5
[5,3,4,1,2] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,6,1,5,4,2] => [6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4
[3,6,2,5,4,1] => [6,4,2,5,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[3,6,4,2,5,1] => [6,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[4,2,6,1,5,3] => [6,2,4,3,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[4,3,6,1,5,2] => [6,3,4,2,5,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[4,3,6,2,5,1] => [6,3,5,2,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[4,5,1,6,2,3] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[4,5,6,1,2,3] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[4,5,6,2,1,3] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[4,6,1,5,3,2] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[4,6,2,5,3,1] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[4,6,3,5,2,1] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[4,6,5,1,2,3] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[4,6,5,2,1,3] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[5,2,6,1,4,3] => [6,2,4,5,3,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[5,3,2,6,1,4] => [6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4
[5,3,6,1,4,2] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[5,3,6,2,4,1] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[5,4,2,6,1,3] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
[5,4,3,6,1,2] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[5,4,6,1,3,2] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[5,4,6,2,3,1] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[5,4,6,3,1,2] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[5,6,1,4,3,2] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[5,6,2,4,3,1] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[5,6,3,4,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[5,6,4,1,3,2] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[5,6,4,2,3,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[5,6,4,3,1,2] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[6,2,5,1,4,3] => [6,4,2,5,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,2,5,3,1,4] => [6,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,3,2,5,1,4] => [6,3,5,2,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,3,5,1,4,2] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[6,3,5,2,4,1] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,4,2,5,1,3] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5
[6,4,3,5,1,2] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,4,5,1,3,2] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,4,5,2,3,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[6,4,5,3,1,2] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[6,5,2,4,1,3] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6
[6,5,3,4,1,2] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[3,5,1,7,4,6,2] => [7,3,2,6,4,5,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2
[3,5,2,7,4,6,1] => [7,4,2,6,3,5,1] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[3,5,7,1,4,6,2] => [7,6,4,2,3,5,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[3,5,7,2,4,6,1] => [7,6,5,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[3,6,1,7,4,5,2] => [7,3,2,6,5,4,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[3,6,2,7,4,5,1] => [7,4,2,6,5,3,1] => ([(0,3),(0,5),(0,6),(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)
=> ? = 6
[3,6,7,1,4,5,2] => [7,6,4,2,5,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 7
[3,6,7,2,4,5,1] => [7,6,5,2,4,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6
[3,7,1,6,5,4,2] => [7,3,2,6,5,4,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[3,7,2,6,5,4,1] => [7,4,2,6,5,3,1] => ([(0,3),(0,5),(0,6),(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)
=> ? = 6
[3,7,4,2,6,5,1] => [7,5,4,2,6,3,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6
[3,7,4,5,1,6,2] => [7,6,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 7
[5,6,7,2,3,4,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[5,6,7,3,1,4,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[5,6,7,4,1,2,3] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[5,7,6,3,2,4,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[5,7,6,4,2,1,3] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,4,7,5,1,2,3] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,5,7,2,4,3,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,5,7,4,1,3,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,7,4,5,3,2,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,7,5,3,4,2,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,7,5,4,2,3,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[6,7,5,4,3,1,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,4,5,6,1,2,3] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,4,6,5,2,1,3] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,5,4,6,1,3,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,5,6,3,4,2,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,5,6,4,2,3,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,5,6,4,3,1,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,6,4,5,2,3,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,6,4,5,3,1,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,6,5,3,4,1,2] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St000454
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00277: Permutations —catalanization⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 71%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,4,1,2] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[4,3,2,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[3,5,1,4,2] => [5,3,2,4,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[3,5,2,4,1] => [5,4,2,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[4,2,5,1,3] => [5,2,4,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[4,3,5,1,2] => [5,3,4,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[4,5,1,3,2] => [5,3,4,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[4,5,2,3,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[4,5,3,1,2] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[5,2,4,1,3] => [5,4,2,3,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[5,3,4,1,2] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4 = 5 - 1
[3,6,1,5,4,2] => [6,3,2,5,4,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[3,6,2,5,4,1] => [6,4,2,5,3,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[3,6,4,2,5,1] => [6,5,4,2,3,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,2,6,1,5,3] => [6,2,4,3,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 - 1
[4,3,6,1,5,2] => [6,3,4,2,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[4,3,6,2,5,1] => [6,3,5,2,4,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,5,1,6,2,3] => [6,3,4,5,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[4,5,6,2,1,3] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,6,1,5,3,2] => [6,3,4,5,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[4,6,2,5,3,1] => [6,4,3,5,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[4,6,3,5,2,1] => [6,5,3,4,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,6,5,1,2,3] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[5,2,6,1,4,3] => [6,2,4,5,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[5,3,2,6,1,4] => [6,3,2,5,4,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
[5,3,6,1,4,2] => [6,3,4,5,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[5,3,6,2,4,1] => [6,3,5,4,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[5,4,2,6,1,3] => [6,3,4,5,2,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2 - 1
[5,4,3,6,1,2] => [6,4,3,5,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[5,4,6,2,3,1] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,4,6,3,1,2] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,1,4,3,2] => [6,3,5,4,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[5,6,2,4,3,1] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[5,6,4,1,3,2] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[6,2,5,1,4,3] => [6,4,2,5,3,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,2,5,3,1,4] => [6,5,4,2,3,1] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,3,2,5,1,4] => [6,3,5,2,4,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,3,5,1,4,2] => [6,4,3,5,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[6,3,5,2,4,1] => [6,5,3,4,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,4,2,5,1,3] => [6,3,5,4,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 5 - 1
[6,4,3,5,1,2] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,4,5,1,3,2] => [6,4,5,3,2,1] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[6,5,2,4,1,3] => [6,5,3,4,2,1] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 6 - 1
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 5 = 6 - 1
[3,5,1,7,4,6,2] => [7,3,2,6,4,5,1] => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2 - 1
[3,5,2,7,4,6,1] => [7,4,2,6,3,5,1] => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4 - 1
[3,5,7,1,4,6,2] => [7,6,4,2,3,5,1] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
[3,5,7,2,4,6,1] => [7,6,5,2,3,4,1] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3 - 1
[3,6,1,7,4,5,2] => [7,3,2,6,5,4,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4 - 1
[3,6,2,7,4,5,1] => [7,4,2,6,5,3,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6 - 1
[3,6,7,1,4,5,2] => [7,6,4,2,5,3,1] => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 7 - 1
[3,6,7,2,4,5,1] => [7,6,5,2,4,3,1] => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6 - 1
[3,7,1,6,5,4,2] => [7,3,2,6,5,4,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4 - 1
[3,7,2,6,5,4,1] => [7,4,2,6,5,3,1] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6 - 1
[3,7,4,2,6,5,1] => [7,5,4,2,6,3,1] => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6 - 1
[3,7,4,5,1,6,2] => [7,6,5,4,2,3,1] => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 7 - 1
[5,6,7,2,3,4,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[5,6,7,3,1,4,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[5,6,7,4,1,2,3] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[5,7,6,3,2,4,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[5,7,6,4,2,1,3] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,4,7,5,1,2,3] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,5,7,2,4,3,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,5,7,4,1,3,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,7,4,5,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,7,5,3,4,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,7,5,4,2,3,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[6,7,5,4,3,1,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,4,5,6,1,2,3] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,4,6,5,2,1,3] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,5,4,6,1,3,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,5,6,3,4,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,5,6,4,2,3,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,5,6,4,3,1,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,6,4,5,2,3,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,6,4,5,3,1,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,6,5,3,4,1,2] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 7 - 1
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St000528
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
Description
The height of a poset.
This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St000907
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000907: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St000907: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
Description
The number of maximal antichains of minimal length in a poset.
Matching statistic: St000911
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000911: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St000911: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
Description
The number of maximal antichains of maximal size in a poset.
Matching statistic: St000912
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000912: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St000912: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
Description
The number of maximal antichains in a poset.
Matching statistic: St001343
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001343: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St001343: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7
Description
The dimension of the reduced incidence algebra of a poset.
The reduced incidence algebra of a poset is the subalgebra of the incidence algebra consisting of the elements which assign the same value to any two intervals that are isomorphic to each other as posets.
Thus, this statistic returns the number of non-isomorphic intervals of the poset.
Matching statistic: St001631
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001631: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St001631: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4 - 1
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 - 1
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5 - 1
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4 - 1
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1 - 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2 - 1
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2 - 1
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2 - 1
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6 - 1
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2 - 1
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4 - 1
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2 - 1
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5 - 1
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2 - 1
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5 - 1
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6 - 1
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6 - 1
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6 - 1
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5 - 1
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2 - 1
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4 - 1
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3 - 1
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3 - 1
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4 - 1
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6 - 1
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7 - 1
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6 - 1
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4 - 1
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6 - 1
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
Description
The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset.
Matching statistic: St001879
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Mp00209: Permutations —pattern poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 71%
Values
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[3,5,1,4,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 4 - 1
[3,5,2,4,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[4,2,5,1,3] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 - 1
[4,3,5,1,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 5 - 1
[4,5,1,3,2] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[5,2,4,1,3] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 - 1
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[3,6,1,5,4,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 4 - 1
[3,6,2,5,4,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[3,6,4,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[4,2,6,1,5,3] => [1,5,2,6,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,21),(2,11),(2,12),(2,19),(3,9),(3,13),(3,19),(4,10),(4,13),(4,19),(5,10),(5,12),(5,14),(5,19),(6,1),(6,9),(6,11),(6,14),(6,19),(8,17),(8,20),(9,18),(9,21),(10,16),(10,21),(11,15),(11,18),(11,21),(12,15),(12,16),(13,21),(14,8),(14,15),(14,16),(14,18),(15,17),(15,20),(16,17),(16,20),(17,7),(18,17),(18,20),(19,16),(19,18),(19,21),(20,7),(21,20)],22)
=> ? = 1 - 1
[4,3,6,1,5,2] => [1,5,2,3,6,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(1,20),(1,21),(2,13),(2,14),(3,8),(3,13),(3,15),(4,9),(4,10),(4,13),(4,15),(5,7),(5,8),(5,9),(5,14),(6,1),(6,7),(6,10),(6,14),(6,15),(7,12),(7,16),(7,18),(7,20),(8,18),(8,21),(9,16),(9,18),(9,21),(10,16),(10,20),(10,21),(12,17),(12,19),(13,21),(14,20),(14,21),(15,18),(15,20),(15,21),(16,17),(16,19),(17,11),(18,17),(18,19),(19,11),(20,17),(20,19),(21,19)],22)
=> ? = 2 - 1
[4,3,6,2,5,1] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
=> ? = 6 - 1
[4,5,1,6,2,3] => [1,6,2,3,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 2 - 1
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[4,5,6,2,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[4,6,1,5,3,2] => [1,5,2,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 2 - 1
[4,6,2,5,3,1] => [1,2,5,3,4,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[4,6,3,5,2,1] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[4,6,5,1,2,3] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[4,6,5,2,1,3] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6 - 1
[5,2,6,1,4,3] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 2 - 1
[5,3,2,6,1,4] => [1,4,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 4 - 1
[5,3,6,1,4,2] => [1,4,2,3,6,5] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2 - 1
[5,3,6,2,4,1] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
=> ? = 5 - 1
[5,4,2,6,1,3] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
=> ? = 2 - 1
[5,4,3,6,1,2] => [1,2,3,6,4,5] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 5 - 1
[5,4,6,1,3,2] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
=> ? = 6 - 1
[5,4,6,2,3,1] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[5,4,6,3,1,2] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 6 - 1
[5,6,1,4,3,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[5,6,2,4,3,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6 - 1
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[5,6,4,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,2,5,1,4,3] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,2,5,3,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,3,2,5,1,4] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
=> ? = 6 - 1
[6,3,5,1,4,2] => [1,4,2,3,5,6] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 5 - 1
[6,3,5,2,4,1] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
=> ? = 6 - 1
[6,4,2,5,1,3] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
=> ? = 5 - 1
[6,4,3,5,1,2] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,4,5,1,3,2] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,4,5,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,4,5,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,5,2,4,1,3] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
=> ? = 6 - 1
[6,5,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 6 - 1
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => ?
=> ? = 2 - 1
[3,5,2,7,4,6,1] => [1,2,7,3,5,4,6] => ?
=> ? = 4 - 1
[3,5,7,1,4,6,2] => [1,4,6,2,3,5,7] => ?
=> ? = 3 - 1
[3,5,7,2,4,6,1] => [1,2,4,6,3,5,7] => ?
=> ? = 3 - 1
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,28),(2,12),(2,13),(2,19),(3,11),(3,13),(3,18),(4,1),(4,14),(4,15),(4,18),(4,19),(5,10),(5,11),(5,14),(5,19),(6,10),(6,12),(6,15),(6,18),(8,17),(8,25),(9,17),(9,26),(10,16),(10,22),(10,23),(11,22),(11,27),(12,23),(12,27),(13,27),(14,8),(14,16),(14,22),(14,28),(15,9),(15,16),(15,23),(15,28),(16,17),(16,25),(16,26),(17,20),(18,22),(18,27),(18,28),(19,23),(19,27),(19,28),(20,7),(21,7),(22,24),(22,25),(23,24),(23,26),(24,21),(25,20),(25,21),(26,20),(26,21),(27,24),(28,24),(28,25),(28,26)],29)
=> ? = 4 - 1
[3,6,2,7,4,5,1] => [1,2,7,3,6,4,5] => ([(0,1),(0,2),(0,3),(0,5),(0,6),(1,12),(1,16),(1,27),(2,11),(2,13),(2,27),(3,13),(3,15),(3,27),(4,8),(4,9),(4,10),(4,26),(5,11),(5,12),(5,14),(5,27),(6,4),(6,14),(6,15),(6,16),(6,27),(8,18),(8,23),(9,18),(9,23),(9,25),(10,23),(10,24),(11,21),(11,22),(12,17),(12,21),(13,22),(14,9),(14,17),(14,21),(14,26),(15,10),(15,22),(15,26),(16,8),(16,17),(16,26),(17,18),(17,25),(18,19),(19,7),(20,7),(21,24),(21,25),(22,24),(23,19),(23,20),(24,20),(25,19),(25,20),(26,23),(26,24),(26,25),(27,21),(27,22),(27,26)],28)
=> ? = 6 - 1
[3,6,7,1,4,5,2] => [1,4,5,2,3,6,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(1,8),(2,12),(2,13),(2,16),(3,1),(3,14),(3,15),(3,16),(4,9),(4,11),(4,13),(4,15),(5,9),(5,11),(5,12),(5,14),(6,22),(6,23),(7,21),(7,22),(7,28),(8,21),(8,23),(8,28),(9,27),(11,17),(11,20),(11,27),(12,17),(12,18),(12,27),(13,17),(13,19),(13,27),(14,7),(14,18),(14,20),(14,27),(15,8),(15,19),(15,20),(15,27),(16,6),(16,18),(16,19),(17,24),(17,28),(18,22),(18,24),(18,28),(19,23),(19,24),(19,28),(20,21),(20,24),(20,28),(21,25),(21,26),(22,25),(22,26),(23,25),(23,26),(24,25),(24,26),(25,10),(26,10),(27,28),(28,26)],29)
=> ? = 7 - 1
[3,6,7,2,4,5,1] => [1,2,4,5,3,6,7] => ([(0,1),(0,4),(0,5),(0,6),(1,20),(2,10),(2,12),(2,23),(3,9),(3,11),(3,23),(4,13),(4,14),(4,20),(5,3),(5,13),(5,15),(5,20),(6,2),(6,14),(6,15),(6,20),(8,19),(8,21),(9,17),(9,22),(10,18),(10,22),(11,8),(11,17),(11,22),(12,8),(12,18),(12,22),(13,9),(13,16),(13,23),(14,10),(14,16),(14,23),(15,11),(15,12),(15,16),(15,23),(16,17),(16,18),(16,22),(17,19),(17,21),(18,19),(18,21),(19,7),(20,23),(21,7),(22,21),(23,22)],24)
=> ? = 6 - 1
[3,7,1,6,5,4,2] => [1,6,2,3,7,4,5] => ?
=> ? = 4 - 1
[3,7,2,6,5,4,1] => [1,2,6,3,7,4,5] => ?
=> ? = 6 - 1
[5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 7 - 1
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
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