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Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000259
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+] => [1] => [1] => ([],1)
=> 0
[-] => [1] => [1] => ([],1)
=> 0
[+,+] => [1,2] => [2,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => [2,1] => ([(0,1)],2)
=> 1
[-,-] => [1,2] => [2,1] => ([(0,1)],2)
=> 1
[+,+,+] => [1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[+,+,-] => [1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[-,+,-] => [2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> 2
[+,-,-] => [1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[-,-,-] => [1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[+,3,2] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[2,1,-] => [2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> 2
[+,+,+,+] => [1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,+,-,+] => [1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,+,+,-] => [1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[-,+,-,+] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[-,+,+,-] => [2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,-,-,+] => [1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,-,+,-] => [1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,+,-,-] => [1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[-,-,+,-] => [3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[-,+,-,-] => [2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[-,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[+,+,4,3] => [1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[-,+,4,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[+,-,4,3] => [1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,3,2,+] => [1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,3,2,-] => [1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[-,3,2,-] => [3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,3,4,2] => [1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,4,2,3] => [1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,4,+,2] => [1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[+,4,-,2] => [1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,1,-,+] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[2,1,+,-] => [2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,1,-,-] => [2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,1,4,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[2,3,1,-] => [3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,1,2,-] => [2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[3,+,1,-] => [2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,-,1,-] => [3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,+,4,1] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[4,1,-,2] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[4,+,-,1] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[+,+,+,+,+] => [1,2,3,4,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[+,-,+,+,+] => [1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001632
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 25% ●values known / values provided: 54%●distinct values known / distinct values provided: 25%
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 25% ●values known / values provided: 54%●distinct values known / distinct values provided: 25%
Values
[+] => [1] => [1] => ([],1)
=> ? = 0 - 3
[-] => [1] => [1] => ([],1)
=> ? = 0 - 3
[+,+] => [1,2] => [2,1] => ([],2)
=> ? = 1 - 3
[+,-] => [1,2] => [2,1] => ([],2)
=> ? = 1 - 3
[-,-] => [1,2] => [2,1] => ([],2)
=> ? = 1 - 3
[+,+,+] => [1,2,3] => [3,2,1] => ([],3)
=> ? = 1 - 3
[+,-,+] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? = 2 - 3
[+,+,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? = 1 - 3
[-,+,-] => [2,1,3] => [2,3,1] => ([(1,2)],3)
=> ? = 2 - 3
[+,-,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? = 1 - 3
[-,-,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? = 1 - 3
[+,3,2] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? = 2 - 3
[2,1,-] => [2,1,3] => [2,3,1] => ([(1,2)],3)
=> ? = 2 - 3
[+,+,+,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? = 1 - 3
[+,-,+,+] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[+,+,-,+] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? = 2 - 3
[+,+,+,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? = 1 - 3
[-,+,-,+] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[-,+,+,-] => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[+,-,-,+] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[+,-,+,-] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? = 2 - 3
[+,+,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? = 1 - 3
[-,-,+,-] => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[-,+,-,-] => [2,1,3,4] => [3,4,2,1] => ([(2,3)],4)
=> ? = 2 - 3
[+,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? = 1 - 3
[-,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? = 1 - 3
[+,+,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? = 2 - 3
[-,+,4,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[+,-,4,3] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[+,3,2,+] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[+,3,2,-] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? = 2 - 3
[-,3,2,-] => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[+,3,4,2] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[+,4,2,3] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[+,4,+,2] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[+,4,-,2] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[2,1,-,+] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[2,1,+,-] => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[2,1,-,-] => [2,1,3,4] => [3,4,2,1] => ([(2,3)],4)
=> ? = 2 - 3
[2,1,4,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[2,3,1,-] => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[3,1,2,-] => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[3,+,1,-] => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? = 2 - 3
[3,-,1,-] => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? = 2 - 3
[3,+,4,1] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[4,1,-,2] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[4,+,-,1] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0 = 3 - 3
[+,+,+,+,+] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> ? = 1 - 3
[+,-,+,+,+] => [1,3,4,5,2] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 3
[+,+,-,+,+] => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> ? = 2 - 3
[+,+,+,-,+] => [1,2,3,5,4] => [5,4,3,1,2] => ([(3,4)],5)
=> ? = 2 - 3
[+,+,+,+,-] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
=> ? = 1 - 3
[-,+,-,+,+] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,+,+,-,+] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,+,+,+,-] => [2,3,4,1,5] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 3
[+,-,-,+,+] => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? = 2 - 3
[+,-,+,-,+] => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
=> ? = 2 - 3
[+,-,+,+,-] => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> ? = 2 - 3
[+,+,-,-,+] => [1,2,5,3,4] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> ? = 2 - 3
[-,-,+,-,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,+,-,-,+] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,+,+,5,4] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,-,+,5,4] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,+,-,5,4] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,+,4,3,+] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,+,4,5,3] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,+,5,3,4] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,+,5,+,3] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[-,+,5,-,3] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,3,2,-,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,3,2,5,4] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,4,2,5,3] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,4,+,5,2] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,5,2,-,3] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[-,5,+,-,2] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,1,-,+,+] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,+,-,+] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,-,-,+] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,1,+,5,4] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,-,5,4] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,1,4,3,+] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,4,5,3] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,1,5,3,4] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,5,+,3] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[2,1,5,-,3] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,3,1,-,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,3,1,5,4] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,4,1,5,3] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,4,+,5,1] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,5,1,-,3] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[2,5,+,-,1] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[3,1,2,-,+] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[3,1,2,5,4] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[3,1,4,2,+] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[3,1,4,5,2] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[3,1,5,2,4] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[3,1,5,+,2] => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
[3,1,5,-,2] => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 0 = 3 - 3
[3,+,1,-,+] => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
=> 0 = 3 - 3
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St000455
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 50%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 50%
Values
[+] => [1] => ([],1)
=> ? = 0 - 2
[-] => [1] => ([],1)
=> ? = 0 - 2
[+,+] => [1,2] => ([],2)
=> ? = 1 - 2
[+,-] => [1,2] => ([],2)
=> ? = 1 - 2
[-,-] => [1,2] => ([],2)
=> ? = 1 - 2
[+,+,+] => [1,2,3] => ([],3)
=> ? = 1 - 2
[+,-,+] => [1,3,2] => ([(1,2)],3)
=> 0 = 2 - 2
[+,+,-] => [1,2,3] => ([],3)
=> ? = 1 - 2
[-,+,-] => [2,1,3] => ([(1,2)],3)
=> 0 = 2 - 2
[+,-,-] => [1,2,3] => ([],3)
=> ? = 1 - 2
[-,-,-] => [1,2,3] => ([],3)
=> ? = 1 - 2
[+,3,2] => [1,3,2] => ([(1,2)],3)
=> 0 = 2 - 2
[2,1,-] => [2,1,3] => ([(1,2)],3)
=> 0 = 2 - 2
[+,+,+,+] => [1,2,3,4] => ([],4)
=> ? = 1 - 2
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
=> 0 = 2 - 2
[+,+,+,-] => [1,2,3,4] => ([],4)
=> ? = 1 - 2
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
=> 0 = 2 - 2
[+,+,-,-] => [1,2,3,4] => ([],4)
=> ? = 1 - 2
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
=> 0 = 2 - 2
[+,-,-,-] => [1,2,3,4] => ([],4)
=> ? = 1 - 2
[-,-,-,-] => [1,2,3,4] => ([],4)
=> ? = 1 - 2
[+,+,4,3] => [1,2,4,3] => ([(2,3)],4)
=> 0 = 2 - 2
[-,+,4,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[+,-,4,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,3,2,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,3,2,-] => [1,3,2,4] => ([(2,3)],4)
=> 0 = 2 - 2
[-,3,2,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,3,4,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,4,2,3] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,4,+,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[+,4,-,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[2,1,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[2,1,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[2,1,-,-] => [2,1,3,4] => ([(2,3)],4)
=> 0 = 2 - 2
[2,1,4,3] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[2,3,1,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[3,1,2,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[3,+,1,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[3,-,1,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> 0 = 2 - 2
[3,+,4,1] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[4,1,-,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[4,+,-,1] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 3 - 2
[+,+,+,+,+] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[+,-,+,+,+] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,+,-,+,+] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,+,+,-,+] => [1,2,3,5,4] => ([(3,4)],5)
=> 0 = 2 - 2
[+,+,+,+,-] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[-,+,+,+,-] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,-,-,+,+] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 2 - 2
[+,-,+,-,+] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[+,-,+,+,-] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,+,-,-,+] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,+,-,+,-] => [1,2,4,3,5] => ([(3,4)],5)
=> 0 = 2 - 2
[+,+,+,-,-] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,-,+,+,-] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 2 - 2
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[-,+,-,+,-] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[-,+,+,-,-] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,-,-,-,+] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,-,-,+,-] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,-,+,-,-] => [1,3,2,4,5] => ([(3,4)],5)
=> 0 = 2 - 2
[+,+,-,-,-] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[-,-,-,+,-] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,-,+,-,-] => [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,+,-,-,-] => [2,1,3,4,5] => ([(3,4)],5)
=> 0 = 2 - 2
[+,-,-,-,-] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[-,-,-,-,-] => [1,2,3,4,5] => ([],5)
=> ? = 1 - 2
[+,+,+,5,4] => [1,2,3,5,4] => ([(3,4)],5)
=> 0 = 2 - 2
[-,+,+,5,4] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[+,-,+,5,4] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[+,+,-,5,4] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,-,+,5,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,-,5,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[+,-,-,5,4] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[+,+,4,3,+] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,+,4,3,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,4,3,+] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 0 = 2 - 2
[+,+,4,3,-] => [1,2,4,3,5] => ([(3,4)],5)
=> 0 = 2 - 2
[-,+,4,3,-] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[+,-,4,3,-] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,-,4,3,-] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> 0 = 2 - 2
[-,+,4,5,3] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[-,+,5,3,4] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,5,+,3] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,5,-,3] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 3 - 2
[+,3,2,-,+] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[-,3,2,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,3,2,5,4] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[-,3,2,5,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,4,2,5,3] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 - 2
[-,4,2,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 3 - 2
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Matching statistic: St000777
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[+] => [1] => [1] => ([],1)
=> 1 = 0 + 1
[-] => [1] => [1] => ([],1)
=> 1 = 0 + 1
[+,+] => [1,2] => [2] => ([],2)
=> ? = 1 + 1
[+,-] => [1,2] => [2] => ([],2)
=> ? = 1 + 1
[-,-] => [1,2] => [2] => ([],2)
=> ? = 1 + 1
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? = 1 + 1
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 3 = 2 + 1
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 + 1
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2 + 1
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 + 1
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 + 1
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 3 = 2 + 1
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2 + 1
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 + 1
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 + 1
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 + 1
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 + 1
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 + 1
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 2 + 1
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[3,1,2,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 + 1
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 + 1
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 + 1
[+,+,+,+,+] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 + 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,+,+,-] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 + 1
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 1
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 1
[-,+,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,+,-,-,+] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,+,-,+,-] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 1
[+,+,+,-,-] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 + 1
[-,-,+,-,+] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 + 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 2 + 1
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,+,-,+] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,5,4,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,6,4,5] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,5,3,4,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,6,3,4,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,5,2,3,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,6,2,3,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 2 + 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St000456
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 25%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 25%
Values
[+] => [1] => [1] => ([],1)
=> ? = 0 - 1
[-] => [1] => [1] => ([],1)
=> ? = 0 - 1
[+,+] => [1,2] => [2] => ([],2)
=> ? = 1 - 1
[+,-] => [1,2] => [2] => ([],2)
=> ? = 1 - 1
[-,-] => [1,2] => [2] => ([],2)
=> ? = 1 - 1
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? = 1 - 1
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 - 1
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2 - 1
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 - 1
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 1 - 1
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2 - 1
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 - 1
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 - 1
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 - 1
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 - 1
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1 - 1
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 2 - 1
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[3,1,2,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2 - 1
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 2 - 1
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[+,+,+,+,+] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 - 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,+,+,-] => [1,2,3,4,5] => [5] => ([],5)
=> ? = 1 - 1
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,+,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,+,-,-,+] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,+,-,+,-] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 - 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 2 - 1
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,+,-,+] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,5,4,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,6,4,5] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,5,3,4,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,6,3,4,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,5,2,3,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,2,3,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,+,2,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 2 - 1
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St001582
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Mp00064: Permutations —reverse⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Values
[+] => [1] => [1] => ? = 0 - 1
[-] => [1] => [1] => ? = 0 - 1
[+,+] => [1,2] => [2,1] => 0 = 1 - 1
[+,-] => [1,2] => [2,1] => 0 = 1 - 1
[-,-] => [1,2] => [2,1] => 0 = 1 - 1
[+,+,+] => [1,2,3] => [3,2,1] => 0 = 1 - 1
[+,-,+] => [1,3,2] => [2,3,1] => 1 = 2 - 1
[+,+,-] => [1,2,3] => [3,2,1] => 0 = 1 - 1
[-,+,-] => [2,1,3] => [3,1,2] => 1 = 2 - 1
[+,-,-] => [1,2,3] => [3,2,1] => 0 = 1 - 1
[-,-,-] => [1,2,3] => [3,2,1] => 0 = 1 - 1
[+,3,2] => [1,3,2] => [2,3,1] => 1 = 2 - 1
[2,1,-] => [2,1,3] => [3,1,2] => 1 = 2 - 1
[+,+,+,+] => [1,2,3,4] => [4,3,2,1] => 0 = 1 - 1
[+,-,+,+] => [1,3,4,2] => [2,4,3,1] => 1 = 2 - 1
[+,+,-,+] => [1,2,4,3] => [3,4,2,1] => 1 = 2 - 1
[+,+,+,-] => [1,2,3,4] => [4,3,2,1] => 0 = 1 - 1
[-,+,-,+] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[-,+,+,-] => [2,3,1,4] => [4,1,3,2] => 1 = 2 - 1
[+,-,-,+] => [1,4,2,3] => [3,2,4,1] => 1 = 2 - 1
[+,-,+,-] => [1,3,2,4] => [4,2,3,1] => 1 = 2 - 1
[+,+,-,-] => [1,2,3,4] => [4,3,2,1] => 0 = 1 - 1
[-,-,+,-] => [3,1,2,4] => [4,2,1,3] => 1 = 2 - 1
[-,+,-,-] => [2,1,3,4] => [4,3,1,2] => 1 = 2 - 1
[+,-,-,-] => [1,2,3,4] => [4,3,2,1] => 0 = 1 - 1
[-,-,-,-] => [1,2,3,4] => [4,3,2,1] => 0 = 1 - 1
[+,+,4,3] => [1,2,4,3] => [3,4,2,1] => 1 = 2 - 1
[-,+,4,3] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[+,-,4,3] => [1,4,2,3] => [3,2,4,1] => 1 = 2 - 1
[+,3,2,+] => [1,3,4,2] => [2,4,3,1] => 1 = 2 - 1
[+,3,2,-] => [1,3,2,4] => [4,2,3,1] => 1 = 2 - 1
[-,3,2,-] => [3,1,2,4] => [4,2,1,3] => 1 = 2 - 1
[+,3,4,2] => [1,4,2,3] => [3,2,4,1] => 1 = 2 - 1
[+,4,2,3] => [1,3,4,2] => [2,4,3,1] => 1 = 2 - 1
[+,4,+,2] => [1,3,4,2] => [2,4,3,1] => 1 = 2 - 1
[+,4,-,2] => [1,4,2,3] => [3,2,4,1] => 1 = 2 - 1
[2,1,-,+] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[2,1,+,-] => [2,3,1,4] => [4,1,3,2] => 1 = 2 - 1
[2,1,-,-] => [2,1,3,4] => [4,3,1,2] => 1 = 2 - 1
[2,1,4,3] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[2,3,1,-] => [3,1,2,4] => [4,2,1,3] => 1 = 2 - 1
[3,1,2,-] => [2,3,1,4] => [4,1,3,2] => 1 = 2 - 1
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[3,+,1,-] => [2,3,1,4] => [4,1,3,2] => 1 = 2 - 1
[3,-,1,-] => [3,1,2,4] => [4,2,1,3] => 1 = 2 - 1
[3,+,4,1] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[4,1,-,2] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[4,+,-,1] => [2,4,1,3] => [3,1,4,2] => 2 = 3 - 1
[+,+,+,+,+] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[+,-,+,+,+] => [1,3,4,5,2] => [2,5,4,3,1] => ? = 2 - 1
[+,+,-,+,+] => [1,2,4,5,3] => [3,5,4,2,1] => ? = 2 - 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,5,3,2,1] => ? = 2 - 1
[+,+,+,+,-] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[-,+,-,+,+] => [2,4,5,1,3] => [3,1,5,4,2] => ? = 3 - 1
[-,+,+,-,+] => [2,3,5,1,4] => [4,1,5,3,2] => ? = 3 - 1
[-,+,+,+,-] => [2,3,4,1,5] => [5,1,4,3,2] => ? = 2 - 1
[+,-,-,+,+] => [1,4,5,2,3] => [3,2,5,4,1] => ? = 2 - 1
[+,-,+,-,+] => [1,3,5,2,4] => [4,2,5,3,1] => ? = 2 - 1
[+,-,+,+,-] => [1,3,4,2,5] => [5,2,4,3,1] => ? = 2 - 1
[+,+,-,-,+] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2 - 1
[+,+,-,+,-] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 2 - 1
[+,+,+,-,-] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[-,-,+,-,+] => [3,5,1,2,4] => [4,2,1,5,3] => ? = 3 - 1
[-,-,+,+,-] => [3,4,1,2,5] => [5,2,1,4,3] => ? = 2 - 1
[-,+,-,-,+] => [2,5,1,3,4] => [4,3,1,5,2] => ? = 3 - 1
[-,+,-,+,-] => [2,4,1,3,5] => [5,3,1,4,2] => ? = 2 - 1
[-,+,+,-,-] => [2,3,1,4,5] => [5,4,1,3,2] => ? = 2 - 1
[+,-,-,-,+] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 2 - 1
[+,-,-,+,-] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2 - 1
[+,-,+,-,-] => [1,3,2,4,5] => [5,4,2,3,1] => ? = 2 - 1
[+,+,-,-,-] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[-,-,-,+,-] => [4,1,2,3,5] => [5,3,2,1,4] => ? = 2 - 1
[-,-,+,-,-] => [3,1,2,4,5] => [5,4,2,1,3] => ? = 2 - 1
[-,+,-,-,-] => [2,1,3,4,5] => [5,4,3,1,2] => ? = 2 - 1
[+,-,-,-,-] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[-,-,-,-,-] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 1 - 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,5,3,2,1] => ? = 2 - 1
[-,+,+,5,4] => [2,3,5,1,4] => [4,1,5,3,2] => ? = 3 - 1
[+,-,+,5,4] => [1,3,5,2,4] => [4,2,5,3,1] => ? = 2 - 1
[+,+,-,5,4] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2 - 1
[-,-,+,5,4] => [3,5,1,2,4] => [4,2,1,5,3] => ? = 3 - 1
[-,+,-,5,4] => [2,5,1,3,4] => [4,3,1,5,2] => ? = 3 - 1
[+,-,-,5,4] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 2 - 1
[+,+,4,3,+] => [1,2,4,5,3] => [3,5,4,2,1] => ? = 2 - 1
[-,+,4,3,+] => [2,4,5,1,3] => [3,1,5,4,2] => ? = 3 - 1
[+,-,4,3,+] => [1,4,5,2,3] => [3,2,5,4,1] => ? = 2 - 1
[+,+,4,3,-] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 2 - 1
[-,+,4,3,-] => [2,4,1,3,5] => [5,3,1,4,2] => ? = 2 - 1
[+,-,4,3,-] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2 - 1
[-,-,4,3,-] => [4,1,2,3,5] => [5,3,2,1,4] => ? = 2 - 1
[+,+,4,5,3] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2 - 1
[-,+,4,5,3] => [2,5,1,3,4] => [4,3,1,5,2] => ? = 3 - 1
[+,-,4,5,3] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 2 - 1
[+,+,5,3,4] => [1,2,4,5,3] => [3,5,4,2,1] => ? = 2 - 1
[-,+,5,3,4] => [2,4,5,1,3] => [3,1,5,4,2] => ? = 3 - 1
[+,-,5,3,4] => [1,4,5,2,3] => [3,2,5,4,1] => ? = 2 - 1
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001860
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001860: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001860: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 75%
Values
[+] => [1] => [1] => [1] => ? = 0 - 1
[-] => [1] => [1] => [1] => ? = 0 - 1
[+,+] => [1,2] => [1,2] => [1,2] => 0 = 1 - 1
[+,-] => [1,2] => [1,2] => [1,2] => 0 = 1 - 1
[-,-] => [1,2] => [1,2] => [1,2] => 0 = 1 - 1
[+,+,+] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[+,-,+] => [1,3,2] => [1,3,2] => [1,3,2] => 1 = 2 - 1
[+,+,-] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-,+,-] => [2,1,3] => [2,1,3] => [2,1,3] => 1 = 2 - 1
[+,-,-] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-,-,-] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[+,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 1 = 2 - 1
[2,1,-] => [2,1,3] => [2,1,3] => [2,1,3] => 1 = 2 - 1
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[+,-,+,+] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,+,-,+] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1 = 2 - 1
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[-,+,-,+] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[-,+,+,-] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[+,-,-,+] => [1,4,2,3] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,-,+,-] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1 = 2 - 1
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[-,-,+,-] => [3,1,2,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[-,+,-,-] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1 = 2 - 1
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1 = 2 - 1
[-,+,4,3] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[+,-,4,3] => [1,4,2,3] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,3,2,+] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,3,2,-] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1 = 2 - 1
[-,3,2,-] => [3,1,2,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[+,3,4,2] => [1,4,2,3] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,4,2,3] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,4,+,2] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[+,4,-,2] => [1,4,2,3] => [1,4,3,2] => [1,4,3,2] => 1 = 2 - 1
[2,1,-,+] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[2,1,+,-] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[2,1,-,-] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1 = 2 - 1
[2,1,4,3] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[2,3,1,-] => [3,1,2,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[3,1,2,-] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[3,1,4,2] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[3,+,1,-] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[3,-,1,-] => [3,1,2,4] => [3,2,1,4] => [3,2,1,4] => 1 = 2 - 1
[3,+,4,1] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[4,1,-,2] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[4,+,-,1] => [2,4,1,3] => [3,4,1,2] => [3,4,1,2] => 2 = 3 - 1
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[+,-,+,+,+] => [1,3,4,5,2] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 2 - 1
[+,+,-,+,+] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[+,+,+,-,+] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 - 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[-,+,-,+,+] => [2,4,5,1,3] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 3 - 1
[-,+,+,-,+] => [2,3,5,1,4] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 3 - 1
[-,+,+,+,-] => [2,3,4,1,5] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 2 - 1
[+,-,-,+,+] => [1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 2 - 1
[+,-,+,-,+] => [1,3,5,2,4] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 2 - 1
[+,-,+,+,-] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => ? = 2 - 1
[+,+,-,-,+] => [1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[+,+,-,+,-] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 2 - 1
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[-,-,+,-,+] => [3,5,1,2,4] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 3 - 1
[-,-,+,+,-] => [3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 2 - 1
[-,+,-,-,+] => [2,5,1,3,4] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 3 - 1
[-,+,-,+,-] => [2,4,1,3,5] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 2 - 1
[-,+,+,-,-] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 2 - 1
[+,-,-,-,+] => [1,5,2,3,4] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 2 - 1
[+,-,-,+,-] => [1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => ? = 2 - 1
[+,-,+,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 2 - 1
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[-,-,-,+,-] => [4,1,2,3,5] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 2 - 1
[-,-,+,-,-] => [3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 2 - 1
[-,+,-,-,-] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 2 - 1
[+,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[-,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 - 1
[-,+,+,5,4] => [2,3,5,1,4] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 3 - 1
[+,-,+,5,4] => [1,3,5,2,4] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 2 - 1
[+,+,-,5,4] => [1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[-,-,+,5,4] => [3,5,1,2,4] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 3 - 1
[-,+,-,5,4] => [2,5,1,3,4] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 3 - 1
[+,-,-,5,4] => [1,5,2,3,4] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 2 - 1
[+,+,4,3,+] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[-,+,4,3,+] => [2,4,5,1,3] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 3 - 1
[+,-,4,3,+] => [1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 2 - 1
[+,+,4,3,-] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 2 - 1
[-,+,4,3,-] => [2,4,1,3,5] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 2 - 1
[+,-,4,3,-] => [1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => ? = 2 - 1
[-,-,4,3,-] => [4,1,2,3,5] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 2 - 1
[+,+,4,5,3] => [1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[-,+,4,5,3] => [2,5,1,3,4] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 3 - 1
[+,-,4,5,3] => [1,5,2,3,4] => [1,5,3,4,2] => [1,5,3,4,2] => ? = 2 - 1
[+,+,5,3,4] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 2 - 1
[-,+,5,3,4] => [2,4,5,1,3] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 3 - 1
[+,-,5,3,4] => [1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 2 - 1
Description
The number of factors of the Stanley symmetric function associated with a signed permutation.
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