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Your data matches 55 different statistics following compositions of up to 3 maps.
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Matching statistic: St000264
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Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000917
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000917: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000917: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 2
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 2
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 2
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 2
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
Description
The open packing number of a graph.
This is the size of a largest subset of vertices of a graph, such that any two distinct vertices in the subset have disjoint open neighbourhood.
Matching statistic: St001672
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001672: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001672: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 2
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 2
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 2
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 2
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 2
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 2
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 2
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 2
Description
The restrained domination number of a graph.
This is the minimal size of a set of vertices $D$ such that every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex not in $D$.
Matching statistic: St000276
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000276: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000276: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 3
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 3
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
Description
The size of the preimage of the map 'to graph' from Ordered trees to Graphs.
Matching statistic: St001479
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001479: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001479: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 3
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 3
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
Description
The number of bridges of a graph.
A bridge is an edge whose removal increases the number of connected components of the graph.
Matching statistic: St001826
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001826: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001826: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 3
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 3
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
Description
The maximal number of leaves on a vertex of a graph.
Matching statistic: St001957
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001957: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001957: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 4 - 3
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => ([(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)
=> ?
=> ? = 3 - 3
[1,2,-7,-6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[1,7,-6,-5,2,3,4] => [1,7,6,5,2,3,4] => ([(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)
=> ?
=> ? = 3 - 3
[-7,1,-4,2,3,5,6] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-6,7,-4,1,2,3,5] => [6,7,4,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 3 - 3
[6,1,2,-7,3,4,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ? = 4 - 3
[-5,1,7,-6,2,3,4] => [5,1,7,6,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
=> ?
=> ? = 3 - 3
[1,5,-7,-4,2,3,6] => [1,5,7,4,2,3,6] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
[-7,-4,6,1,2,3,5] => [7,4,6,1,2,3,5] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 3 - 3
Description
The number of Hasse diagrams with a given underlying undirected graph.
In particular, this statistic vanishes if the graph contains a triangle.
This is the size of the preimage of [[Mp00074]].
Matching statistic: St001570
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 85%●distinct values known / distinct values provided: 50%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 85%●distinct values known / distinct values provided: 50%
Values
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,-2,-1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-1,-4,-3,-2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-2,-4,-3,-1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,-2,-1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[-3,2,1,-4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,4,1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,4,-1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,4,-1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,-4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,-4,1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,-4,-1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[3,-4,-1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,4,1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,4,-1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,4,-1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,-4,1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,-4,1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,-4,-1,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[-3,-4,-1,-2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,-5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,-5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,-5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,4,-5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,-5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,-5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,-5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[1,-4,-5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,-5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,-5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,-5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,4,-5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,-5,2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,-5,2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,-5,-2,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[-1,-4,-5,-2,-3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[2,4,5,1,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
[2,4,5,1,-3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ? = 4 - 3
Description
The minimal number of edges to add to make a graph Hamiltonian.
A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
Matching statistic: St000993
Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 77% ●values known / values provided: 77%●distinct values known / distinct values provided: 100%
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 77% ●values known / values provided: 77%●distinct values known / distinct values provided: 100%
Values
[3,2,1] => [1,2,3] => [1,2,3] => [3]
=> 1 = 3 - 2
[3,2,-1] => [-1,2,3] => [1,2,3] => [3]
=> 1 = 3 - 2
[3,-2,1] => [1,-2,3] => [1,2,3] => [3]
=> 1 = 3 - 2
[3,-2,-1] => [-1,-2,3] => [1,2,3] => [3]
=> 1 = 3 - 2
[-3,2,1] => [1,2,-3] => [1,2,3] => [3]
=> 1 = 3 - 2
[-3,2,-1] => [-1,2,-3] => [1,2,3] => [3]
=> 1 = 3 - 2
[-3,-2,1] => [1,-2,-3] => [1,2,3] => [3]
=> 1 = 3 - 2
[-3,-2,-1] => [-1,-2,-3] => [1,2,3] => [3]
=> 1 = 3 - 2
[1,4,3,2] => [2,3,4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,4,3,-2] => [-2,3,4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,4,-3,2] => [2,-3,4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,4,-3,-2] => [-2,-3,4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,-4,3,2] => [2,3,-4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,-4,3,-2] => [-2,3,-4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,-4,-3,2] => [2,-3,-4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[1,-4,-3,-2] => [-2,-3,-4,1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,4,3,2] => [2,3,4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,4,3,-2] => [-2,3,4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,4,-3,2] => [2,-3,4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,4,-3,-2] => [-2,-3,4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,-4,3,2] => [2,3,-4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,-4,3,-2] => [-2,3,-4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,-4,-3,2] => [2,-3,-4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[-1,-4,-3,-2] => [-2,-3,-4,-1] => [2,3,4,1] => [3,1]
=> 1 = 3 - 2
[2,4,3,1] => [1,3,4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,4,3,-1] => [-1,3,4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,4,-3,1] => [1,-3,4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,4,-3,-1] => [-1,-3,4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,-4,3,1] => [1,3,-4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,-4,3,-1] => [-1,3,-4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,-4,-3,1] => [1,-3,-4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[2,-4,-3,-1] => [-1,-3,-4,2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,4,3,1] => [1,3,4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,4,3,-1] => [-1,3,4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,4,-3,1] => [1,-3,4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,4,-3,-1] => [-1,-3,4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,-4,3,1] => [1,3,-4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,-4,3,-1] => [-1,3,-4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,-4,-3,1] => [1,-3,-4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[-2,-4,-3,-1] => [-1,-3,-4,-2] => [1,3,4,2] => [3,1]
=> 1 = 3 - 2
[3,2,1,4] => [4,1,2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,2,1,-4] => [-4,1,2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,2,-1,4] => [4,-1,2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,2,-1,-4] => [-4,-1,2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,-2,1,4] => [4,1,-2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,-2,1,-4] => [-4,1,-2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,-2,-1,4] => [4,-1,-2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[3,-2,-1,-4] => [-4,-1,-2,3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[-3,2,1,4] => [4,1,2,-3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[-3,2,1,-4] => [-4,1,2,-3] => [4,1,2,3] => [3,1]
=> 1 = 3 - 2
[1,2,5,6,3,4] => [4,3,6,5,2,1] => ? => ?
=> ? = 4 - 2
[1,4,5,2,3,6] => [6,3,2,5,4,1] => ? => ?
=> ? = 4 - 2
[1,4,5,6,2,3] => [3,2,6,5,4,1] => ? => ?
=> ? = 4 - 2
[1,5,6,2,3,4] => [4,3,2,6,5,1] => ? => ?
=> ? = 4 - 2
[1,6,2,5,3,4] => [4,3,5,2,6,1] => ? => ?
=> ? = 3 - 2
[1,6,4,2,3,5] => [5,3,2,4,6,1] => ? => ?
=> ? = 3 - 2
[1,6,4,5,2,3] => [3,2,5,4,6,1] => ? => ?
=> ? = 3 - 2
[3,1,5,6,2,4] => [4,2,6,5,1,3] => ? => ?
=> ? = 4 - 2
[3,4,1,2,5,6] => [6,5,2,1,4,3] => ? => ?
=> ? = 4 - 2
[3,4,1,6,2,5] => [5,2,6,1,4,3] => ? => ?
=> ? = 4 - 2
[3,4,5,1,2,6] => [6,2,1,5,4,3] => ? => ?
=> ? = 4 - 2
[3,4,5,6,1,2] => [2,1,6,5,4,3] => ? => ?
=> ? = 4 - 2
[3,4,6,1,2,5] => [5,2,1,6,4,3] => ? => ?
=> ? = 4 - 2
[3,5,1,2,4,6] => [6,4,2,1,5,3] => ? => ?
=> ? = 4 - 2
[3,5,6,1,2,4] => [4,2,1,6,5,3] => ? => ?
=> ? = 4 - 2
[3,6,1,2,4,5] => [5,4,2,1,6,3] => ? => ?
=> ? = 4 - 2
[3,6,1,5,2,4] => [4,2,5,1,6,3] => ? => ?
=> ? = 3 - 2
[3,6,4,1,2,5] => [5,2,1,4,6,3] => ? => ?
=> ? = 3 - 2
[3,6,4,5,1,2] => [2,1,5,4,6,3] => ? => ?
=> ? = 3 - 2
[4,5,1,2,3,6] => [6,3,2,1,5,4] => ? => ?
=> ? = 4 - 2
[4,5,6,1,2,3] => [3,2,1,6,5,4] => ? => ?
=> ? = 4 - 2
[4,6,1,2,3,5] => [5,3,2,1,6,4] => ? => ?
=> ? = 4 - 2
[4,6,5,1,2,3] => [3,2,1,5,6,4] => ? => ?
=> ? = 3 - 2
[5,1,2,6,3,4] => [4,3,6,2,1,5] => ? => ?
=> ? = 4 - 2
[5,1,4,2,3,6] => [6,3,2,4,1,5] => ? => ?
=> ? = 3 - 2
[5,1,4,6,2,3] => [3,2,6,4,1,5] => ? => ?
=> ? = 3 - 2
[5,1,6,2,3,4] => [4,3,2,6,1,5] => ? => ?
=> ? = 4 - 2
[5,3,1,2,4,6] => [6,4,2,1,3,5] => ? => ?
=> ? = 3 - 2
[5,3,1,6,2,4] => [4,2,6,1,3,5] => ? => ?
=> ? = 3 - 2
[5,3,4,1,2,6] => [6,2,1,4,3,5] => ? => ?
=> ? = 3 - 2
[5,3,4,6,1,2] => [2,1,6,4,3,5] => ? => ?
=> ? = 3 - 2
[5,6,1,2,3,4] => [4,3,2,1,6,5] => ? => ?
=> ? = 4 - 2
[5,6,1,4,2,3] => [3,2,4,1,6,5] => ? => ?
=> ? = 3 - 2
[5,6,3,1,2,4] => [4,2,1,3,6,5] => ? => ?
=> ? = 3 - 2
[5,6,3,4,1,2] => [2,1,4,3,6,5] => ? => ?
=> ? = 3 - 2
[6,2,1,5,3,4] => [4,3,5,1,2,6] => ? => ?
=> ? = 3 - 2
[6,2,4,1,3,5] => [5,3,1,4,2,6] => ? => ?
=> ? = 3 - 2
[6,3,1,2,4,5] => [5,4,2,1,3,6] => ? => ?
=> ? = 3 - 2
[1,2,7,3,6,4,5] => [5,4,6,3,7,2,1] => ? => ?
=> ? = 3 - 2
[1,4,7,2,3,5,6] => [6,5,3,2,7,4,1] => ? => ?
=> ? = 4 - 2
[1,5,7,2,3,4,6] => [6,4,3,2,7,5,1] => ? => ?
=> ? = 4 - 2
[1,6,7,2,3,4,5] => [5,4,3,2,7,6,1] => ? => ?
=> ? = 4 - 2
[1,6,7,2,5,3,4] => [4,3,5,2,7,6,1] => ? => ?
=> ? = 3 - 2
[1,6,7,4,2,3,5] => [5,3,2,4,7,6,1] => ? => ?
=> ? = 3 - 2
[3,1,7,5,2,4,6] => [6,4,2,5,7,1,3] => ? => ?
=> ? = 3 - 2
[3,4,7,1,2,5,6] => [6,5,2,1,7,4,3] => ? => ?
=> ? = 4 - 2
[3,4,7,1,6,2,5] => [5,2,6,1,7,4,3] => ? => ?
=> ? = 3 - 2
[3,4,7,5,1,2,6] => [6,2,1,5,7,4,3] => ? => ?
=> ? = 3 - 2
[3,4,7,5,6,1,2] => [2,1,6,5,7,4,3] => ? => ?
=> ? = 3 - 2
[3,5,7,1,2,4,6] => [6,4,2,1,7,5,3] => ? => ?
=> ? = 4 - 2
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St000259
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 38% ●values known / values provided: 38%●distinct values known / distinct values provided: 50%
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 38% ●values known / values provided: 38%●distinct values known / distinct values provided: 50%
Values
[3,2,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,2,-1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,-2,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,-2,-1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[-3,2,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[-3,2,-1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[-3,-2,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[-3,-2,-1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[1,4,3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,4,3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,4,-3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,4,-3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,-4,3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,-4,3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,-4,-3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,-4,-3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,4,3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,4,3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,4,-3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,4,-3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,-4,3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,-4,3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,-4,-3,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-1,-4,-3,-2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,-3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,-3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,-4,3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,-4,3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,-4,-3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,-4,-3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,4,3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,4,3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,4,-3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,4,-3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,-4,3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,-4,3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,-4,-3,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-2,-4,-3,-1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,2,1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,-1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,-1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,-1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,-1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,-1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,-1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,-1,4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,-1,-4] => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,-4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,2,-4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,-4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,-2,-4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,-4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,2,-4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,-4,1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-3,-2,-4,-1] => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,4,1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,4,1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,4,-1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,4,-1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,-4,1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,-4,1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,-4,-1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,-4,-1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,4,1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,4,1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,4,-1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,4,-1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,-4,1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,-4,1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,-4,-1,2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[-3,-4,-1,-2] => [3,4,1,2] => [4] => ([],4)
=> ? = 4 - 1
[3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,2,-1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,-2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,-2,-1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,-4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,-4,2,-1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,-4,-2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,-4,-2,-1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[-3,4,2,-1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,2,1,3] => [4,2,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[4,2,1,-3] => [4,2,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
The following 45 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000260The radius of a connected graph. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001851The number of Hecke atoms of a signed permutation. St000068The number of minimal elements in a poset. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001301The first Betti number of the order complex associated with the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001768The number of reduced words of a signed permutation. St000298The order dimension or Dushnik-Miller dimension of a poset. St000640The rank of the largest boolean interval in a poset. St000907The number of maximal antichains of minimal length in a poset. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001399The distinguishing number of a poset. St000717The number of ordinal summands of a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000911The number of maximal antichains of maximal size in a poset. St001268The size of the largest ordinal summand in the poset. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001510The number of self-evacuating linear extensions of a finite poset. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St000656The number of cuts of a poset. St001717The largest size of an interval in a poset. St001490The number of connected components of a skew partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001645The pebbling number of a connected graph. St001964The interval resolution global dimension of a poset. St000181The number of connected components of the Hasse diagram for the poset. St000635The number of strictly order preserving maps of a poset into itself. St001890The maximum magnitude of the Möbius function of a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000417The size of the automorphism group of the ordered tree. St000679The pruning number of an ordered tree. St001058The breadth of the ordered tree.
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