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Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St001548
St001548: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 0
[-,+] => 1
[+,-] => 2
[-,-] => 3
[2,1] => 1
[+,+,+] => 0
[-,+,+] => 1
[+,-,+] => 2
[+,+,-] => 3
[-,-,+] => 3
[-,+,-] => 4
[+,-,-] => 5
[-,-,-] => 6
[+,3,2] => 2
[-,3,2] => 3
[2,1,+] => 1
[2,1,-] => 4
[2,3,1] => 1
[3,1,2] => 3
[3,+,1] => 1
[3,-,1] => 3
[+,+,+,+] => 0
[-,+,+,+] => 1
[+,-,+,+] => 2
[+,+,-,+] => 3
[+,+,+,-] => 4
[-,-,+,+] => 3
[-,+,-,+] => 4
[-,+,+,-] => 5
[+,-,-,+] => 5
[+,-,+,-] => 6
[+,+,-,-] => 7
[-,-,-,+] => 6
[-,-,+,-] => 7
[-,+,-,-] => 8
[+,-,-,-] => 9
[-,-,-,-] => 10
[+,+,4,3] => 3
[-,+,4,3] => 4
[+,-,4,3] => 5
[-,-,4,3] => 6
[+,3,2,+] => 2
[-,3,2,+] => 3
[+,3,2,-] => 6
[-,3,2,-] => 7
[+,3,4,2] => 2
[-,3,4,2] => 3
[+,4,2,3] => 5
[-,4,2,3] => 6
[+,4,+,2] => 2
Description
The sum of the indices of the first term of the associated Grassmann necklace.
Here, we use Postnikov's map (p.59) from decorated permutations to Grassmann necklaces.
Matching statistic: St000777
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 27%●distinct values known / distinct values provided: 25%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 27%●distinct values known / distinct values provided: 25%
Values
[+,+] => [1,2] => [2] => ([],2)
=> ? ∊ {0,1,1,3}
[-,+] => [2,1] => [1,1] => ([(0,1)],2)
=> 2
[+,-] => [1,2] => [2] => ([],2)
=> ? ∊ {0,1,1,3}
[-,-] => [1,2] => [2] => ([],2)
=> ? ∊ {0,1,1,3}
[2,1] => [1,2] => [2] => ([],2)
=> ? ∊ {0,1,1,3}
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 3
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 3
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,-,+] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,3,2] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,3,2] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[2,1,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 3
[2,1,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[2,3,1] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,1,2] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,+,1] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,-,1] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 3
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,+] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,4,3] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[-,3,2,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,4,2] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [3,2,1,4] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,-,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[-,4,-,2] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[2,1,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[2,1,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,4,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,3,1,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,3,1,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,3,4,1] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,4,1,3] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,4,-,1] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[3,1,2,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[3,+,1,+] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,-,1,+] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[4,1,-,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[4,-,1,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[4,-,+,1] => [3,1,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,+,-,1] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,1,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3
[4,3,2,1] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,4,3,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,+,5,-,3] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,+,5,-,3] => [2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,-,5,-,3] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,-,5,-,3] => [3,1,2,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[+,3,2,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,3,5,-,2] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,3,5,-,2] => [2,1,3,5,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[+,4,2,3,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[+,4,+,2,+] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,4,-,2,+] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,-,2,+] => [2,5,1,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,5,2,-,3] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,2,-,3] => [2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,5,-,2,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,-,2,4] => [2,4,1,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,5,-,+,2] => [1,4,2,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,5,+,-,2] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,5,-,+,2] => [4,2,1,5,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[-,5,+,-,2] => [3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[+,5,4,2,3] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,4,2,3] => [2,3,1,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[+,5,4,3,2] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,5,4,3,2] => [3,2,1,5,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St000264
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 14%●distinct values known / distinct values provided: 12%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 14%●distinct values known / distinct values provided: 12%
Values
[+,+] => [1,2] => ([],2)
=> ? ∊ {0,1,1,2,3}
[-,+] => [2,1] => ([(0,1)],2)
=> ? ∊ {0,1,1,2,3}
[+,-] => [1,2] => ([],2)
=> ? ∊ {0,1,1,2,3}
[-,-] => [1,2] => ([],2)
=> ? ∊ {0,1,1,2,3}
[2,1] => [1,2] => ([],2)
=> ? ∊ {0,1,1,2,3}
[+,+,+] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[+,-,+] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[+,+,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[-,+,-] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[+,-,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[-,-,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[+,3,2] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[-,3,2] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[2,1,+] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[2,1,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[2,3,1] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[3,1,2] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[3,+,1] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[3,-,1] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,3,3,3,3,4,4,5,6}
[+,+,+,+] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,+,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,+] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,4,3] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,4,2] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[+,4,-,2] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[3,-,1,+] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[-,-,+,+,+] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[+,-,-,+,+] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,-,+,+] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,-,+,+,-] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,+,5,4] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,-,5,3,4] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,+,5,+,3] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,5,+,3] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,-,5,+,3] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,3,5,+,2] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,+,2,+] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[+,4,-,2,+] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[-,4,+,2,-] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,4,+,5,2] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,4,5,3,2] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,5,2,+,3] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,+,2,4] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,+,+,2] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,-,+,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,+,-,2] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,4,3,2] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
[2,1,-,+,+] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,5,+,3] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[2,3,1,+,+] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,4,-,1,+] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,5,1,+,3] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[2,5,+,+,1] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,-,1,+,+] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,-,1,-,+] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,-,1,+,-] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[3,-,1,5,4] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[3,-,4,1,+] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,-,5,1,4] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[3,-,5,+,1] => [4,1,3,2,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,1,-,2,+] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> 3
[4,-,1,3,+] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,-,+,1,+] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[4,+,-,1,+] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
[4,-,-,1,+] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,3,1,2,+] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> 3
[4,3,2,1,+] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> 3
[4,5,+,2,1] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 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: St001880
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 19%
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 19%
Values
[+,+] => [1,2] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1,1,2,3}
[-,+] => [2,1] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[+,-] => [1,2] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1,1,2,3}
[-,-] => [1,2] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1,1,2,3}
[2,1] => [2,1] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[+,+,+] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,+] => [2,3,1] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,-,+] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,+,-] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,+] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,+,-] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,-,-] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,-] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,3,2] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[-,3,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[2,1,+] => [2,3,1] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[2,1,-] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[2,3,1] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,+,1] => [2,3,1] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[3,-,1] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,1,2,2,3,4,4,5,6}
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,+,+] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,+] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,+] => [1,2,4,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,+,+] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,+] => [2,4,1,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,-] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,3,2,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,-,+] => [4,1,2,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,-] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[-,+,-,-] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,4,3] => [1,2,4,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [2,4,1,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [4,1,2,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,+] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,-] => [1,3,2,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[+,3,4,2] => [1,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [4,1,2,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,-,2] => [1,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,-,2] => [4,1,2,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,+] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,+] => [2,4,1,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,-] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,-] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,4,3] => [2,4,1,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,3,1,+] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,3,1,-] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[2,3,4,1] => [4,1,2,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,4,1,3] => [3,4,1,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[3,-,1,-] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[-,-,+,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[+,-,-,+,-] => [1,4,2,3,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[-,-,-,+,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[-,-,+,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[+,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[-,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[+,-,4,3,-] => [1,4,2,3,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[-,-,4,3,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[-,3,2,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[-,3,2,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[+,3,4,2,-] => [1,4,2,3,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[-,3,4,2,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[-,4,2,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[-,4,+,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[+,4,-,2,-] => [1,4,2,3,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[-,4,-,2,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[2,3,1,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[2,3,1,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[2,3,4,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[2,4,1,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[2,4,+,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[2,4,-,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[3,-,1,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[3,-,1,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[3,-,4,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[3,4,1,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[3,4,2,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[4,-,1,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[4,-,+,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[4,-,-,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[4,3,1,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[4,3,2,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000259
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 25%
Values
[+,+] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[-,+] => [2,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[-,-] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[2,1] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[+,+,+] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[+,-,+] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,+,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3)
=> 2
[-,+,-] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,-,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,-,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,3,2] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,3,2] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,1,+] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,1,-] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,3,1] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[3,1,2] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[3,+,1] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[3,-,1] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,+,+,+] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,+,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,+] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 3
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 2
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,4,3] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 3
[+,3,2,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,4,2] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,-,2] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,-,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,-] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,-] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,4,3] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[4,-,+,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[-,+,+,+,+] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[-,-,+,+,+] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,-,-,+,+] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,-,-,-,+] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[-,+,4,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[-,3,2,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,3,4,2,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,4,2,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[-,4,+,2,+] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,-,2,4] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[-,5,-,+,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,4,+,1,+] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[2,5,-,+,1] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[4,-,+,1,+] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[5,-,+,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[5,-,+,+,1] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[5,+,-,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[5,-,-,+,1] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[5,-,+,-,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[5,-,4,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[5,3,2,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000456
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 50%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 50%
Values
[+,+] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[-,+] => [2,1] => [2,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[-,-] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[2,1] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,1,2,3}
[+,+,+] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[-,+,+] => [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[+,+,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[-,-,+] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[-,+,-] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[+,-,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[-,-,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[+,3,2] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[-,3,2] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[2,1,+] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[2,1,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[2,3,1] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[3,1,2] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[3,+,1] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[3,-,1] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,2,2,3,3,3,3,4,4,5,6}
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,+] => [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,+] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,+] => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 1
[-,+,-,+] => [2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[-,+,+,-] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,+] => [4,1,2,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[-,-,+,-] => [3,1,2,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,-] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,4,3] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [3,1,2,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,+] => [2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[+,3,2,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,4,2] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,-,2] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,-,2] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,+] => [1,3,4,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,+] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,+,-] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[2,1,4,3] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[4,-,+,1] => [3,1,4,2] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[-,+,+,+,+] => [2,3,4,5,1] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[-,-,+,+,+] => [3,4,5,1,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,+,-,+,+] => [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
[-,+,+,-,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,-,-,+,+] => [4,5,1,2,3] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,-,+,-,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[-,+,-,-,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
[-,-,-,-,+] => [5,1,2,3,4] => [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)
=> 10
[-,+,4,3,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,-,4,3,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[-,3,2,+,+] => [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
[-,3,2,-,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
[-,3,4,2,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
[-,4,2,3,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[-,4,+,2,+] => [3,2,5,1,4] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,-,2,+] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 6
[-,5,-,2,4] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,-,+,2] => [4,2,1,5,3] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[2,4,+,1,+] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
[2,5,-,+,1] => [4,1,2,5,3] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[4,-,+,1,+] => [3,1,5,4,2] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[5,-,+,1,4] => [3,1,4,5,2] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[5,-,+,+,1] => [3,4,1,5,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
[5,+,-,+,1] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[5,-,-,+,1] => [4,1,5,2,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[5,-,+,-,1] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
[5,-,4,3,1] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
[5,3,2,+,1] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
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: St001879
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 38%
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 38%
Values
[+,+] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[-,+] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[+,-] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[-,-] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,1,1,2,3}
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> ? ∊ {0,1,1,2,3}
[+,+,+] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,+,+] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,-,+] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,+,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,-,+] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,+,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,-,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,-,-] => [1,2,3] => [3,2,1] => ([],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[+,3,2] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[-,3,2] => [1,3,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,1,+] => [2,1,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,1,-] => [2,1,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[2,3,1] => [2,3,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[3,1,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> ? ∊ {0,1,1,1,1,3,3,3,3,3,4,4,5,6}
[3,+,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[3,-,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[+,+,+,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,+,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,+,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,+,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,+] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,+,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,-,-] => [1,2,3,4] => [4,3,2,1] => ([],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,+,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,+,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,-,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,-,4,3] => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,+] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,+] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,2,-] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,2,-] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,3,4,2] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,3,4,2] => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,2,3] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,2,3] => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,+,2] => [1,4,3,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[-,4,+,2] => [1,4,3,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[+,4,-,2] => [1,4,3,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {0,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,9,10}
[4,+,+,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,-,+,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,+,-,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,-,-,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[5,+,+,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,+,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,-,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,+,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,-,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,+,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,-,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,-,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,-,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,2,+,1] => [5,3,2,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,2,-,1] => [5,3,2,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,4,2,1] => [5,3,4,2,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,4,2,3,1] => [5,4,2,3,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,4,+,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[5,4,-,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
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