Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St001543
Mapping
St001543: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 1
[-,+] => 3
[+,-] => 1
[-,-] => 1
[2,1] => 1
[+,+,+] => 1
[-,+,+] => 4
[+,-,+] => 4
[+,+,-] => 2
[-,-,+] => 4
[-,+,-] => 4
[+,-,-] => 2
[-,-,-] => 1
[+,3,2] => 2
[-,3,2] => 2
[2,1,+] => 2
[2,1,-] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,+,1] => 2
[3,-,1] => 2
[+,+,+,+] => 1
[-,+,+,+] => 5
[+,-,+,+] => 5
[+,+,-,+] => 5
[+,+,+,-] => 3
[-,-,+,+] => 5
[-,+,-,+] => 5
[-,+,+,-] => 5
[+,-,-,+] => 5
[+,-,+,-] => 5
[+,+,-,-] => 3
[-,-,-,+] => 5
[-,-,+,-] => 5
[-,+,-,-] => 5
[+,-,-,-] => 3
[-,-,-,-] => 1
[+,+,4,3] => 3
[-,+,4,3] => 5
[+,-,4,3] => 3
[-,-,4,3] => 3
[+,3,2,+] => 3
[-,3,2,+] => 3
[+,3,2,-] => 3
[-,3,2,-] => 3
[+,3,4,2] => 2
[-,3,4,2] => 2
[+,4,2,3] => 2
[-,4,2,3] => 3
[+,4,+,2] => 3
Description
The largest step for the associated bounded affine permutation. The largest step is the largest distance between any two consecutive terms.
Matching statistic: St000264
(load all 3 compositions to match this statistic)
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 24%●distinct values known / distinct values provided: 17%
Values
[+,+] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,1,1,3}
[-,+] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,1,1,3}
[+,-] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,1,1,3}
[-,-] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,1,1,3}
[2,1] => [2,1] => [2] => ([],2)
 => ? ∊ {1,1,1,1,3}
[+,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,+] => [2,1,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,-] => [2,1,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,3,1] => [2,3,1] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,1,2] => [3,1,2] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[-,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[+,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[-,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[2,1,+,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[+,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,3,2,5,4] => [1,3,2,5,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,3,2,5,4] => [1,3,2,5,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,2,5,3] => [1,4,2,5,3] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,2,5,3] => [1,4,2,5,3] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,+,2,+] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,+,2,+] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,-,2,+] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,+,2,-] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,-,2,+] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,+,2,-] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,-,2,-] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,-,2,-] => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,+,5,2] => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,+,5,2] => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,-,5,2] => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,-,5,2] => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,+,2,4] => [1,5,3,2,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,+,2,4] => [1,5,3,2,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,-,2,4] => [1,5,3,2,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,-,2,4] => [1,5,3,2,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[-,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[+,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(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
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => [1] => ([],1)
 => ? ∊ {1,1,1,1,3}
[-,+] => [1,2] => [1] => ([],1)
 => ? ∊ {1,1,1,1,3}
[+,-] => [1,2] => [1] => ([],1)
 => ? ∊ {1,1,1,1,3}
[-,-] => [1,2] => [1] => ([],1)
 => ? ∊ {1,1,1,1,3}
[2,1] => [2,1] => [1] => ([],1)
 => ? ∊ {1,1,1,1,3}
[+,+,+] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,+] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,+] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,-] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,+] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,-] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,3,2] => [1,3,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,3,2] => [1,3,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,+] => [2,1,3] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,-] => [2,1,3] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,3,1] => [2,3,1] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,1,2] => [3,1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,+,1] => [3,2,1] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,-,1] => [3,2,1] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,+,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,-,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,+,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,+,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,-,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,+,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,+,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,-,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,-,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,+,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,-,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,-,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,+,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,-,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,-,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,+,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,+,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,-,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,-,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,3,2,+] => [1,3,2,4] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,+] => [1,3,2,4] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,-] => [1,3,2,4] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [1,3,2,4] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,3,4,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [1,3,4,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,4,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[-,4,2,3] => [1,4,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,4,+,2] => [1,4,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,+,2] => [1,4,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,-,2] => [1,4,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,-,2] => [1,4,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,+] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,+] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,-] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,-] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,3] => [2,1,4,3] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,+] => [2,3,1,4] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,-] => [2,3,1,4] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,1] => [2,3,4,1] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,1,3] => [2,4,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,+,1] => [2,4,3,1] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,-,1] => [2,4,3,1] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,+] => [3,1,2,4] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,-] => [3,1,2,4] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,4,2] => [3,1,4,2] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,+,1,+] => [3,2,1,4] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,-,1,+] => [3,2,1,4] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,+,1,-] => [3,2,1,4] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,-,1,-] => [3,2,1,4] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,+,4,1] => [3,2,4,1] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,2,3] => [4,1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000259
(load all 6 compositions to match this statistic)
Mapping
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,3}
[-,+] => [2,1] => [1,1] => ([(0,1)],2)
 => 1
[+,-] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,3}
[-,-] => [1,2] => [2] => ([],2)
 => ? ∊ {1,1,3}
[2,1] => [2,1] => [1,1] => ([(0,1)],2)
 => 1
[+,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[+,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[-,-,+] => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[-,3,2] => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[2,1,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[2,3,1] => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[3,1,2] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,+] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,4,3] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[-,4,2,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,1,2,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,2,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,1,2,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,1,2,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(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: St000260
(load all 2 compositions to match this statistic)
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => ([],2)
 => ? ∊ {1,1,1,3}
[-,+] => [2,1] => ([(0,1)],2)
 => 1
[+,-] => [1,2] => ([],2)
 => ? ∊ {1,1,1,3}
[-,-] => [1,2] => ([],2)
 => ? ∊ {1,1,1,3}
[2,1] => [1,2] => ([],2)
 => ? ∊ {1,1,1,3}
[+,+,+] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[+,-,+] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,-] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[-,+,-] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,3,2] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,3,2] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,+] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,-] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,3,1] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,1,2] => [1,2,3] => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,+,1] => [2,1,3] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,-,1] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,+,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,+] => [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)
 => 2
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 1
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,4,3] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,4,3] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,4,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,+] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[+,3,2,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,2,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,+,2] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,+,2] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,-,2] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,-,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,-] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,-] => [1,2,3,4] => ([],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,3] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,-,+,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[-,+,+,+,+] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[-,-,+,+,+] => [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)
 => 2
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,-,-,+,+] => [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)
 => 2
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,-,-,-,+] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[-,+,4,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[-,3,2,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,3,4,2,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,4,2,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[-,4,+,2,+] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,5,-,2,4] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[-,5,-,+,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[2,4,+,1,+] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[2,5,-,+,1] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[4,-,+,1,+] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,-,+,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[5,-,+,+,1] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[5,+,-,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[5,-,-,+,1] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[5,-,+,-,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[5,-,4,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
[5,3,2,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000456
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 50%
Values
[+,+] => [1,2] => ([],2)
 => ([],2)
 => ? ∊ {1,1,1,3}
[-,+] => [2,1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[+,-] => [1,2] => ([],2)
 => ([],2)
 => ? ∊ {1,1,1,3}
[-,-] => [1,2] => ([],2)
 => ([],2)
 => ? ∊ {1,1,1,3}
[2,1] => [1,2] => ([],2)
 => ([],2)
 => ? ∊ {1,1,1,3}
[+,+,+] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
[+,-,+] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,-] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
[-,+,-] => [2,1,3] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,3,2] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[-,3,2] => [2,1,3] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,+] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,1,-] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[2,3,1] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,1,2] => [1,2,3] => ([],3)
 => ([],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,+,1] => [2,1,3] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[3,-,1] => [1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => ? ∊ {1,1,2,2,2,2,2,2,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,+,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,+] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,4,3] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,4,3] => [1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,4,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,+] => [1,2,4,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[+,3,2,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [2,1,3,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [2,1,3,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,2,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,+,2] => [1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,+,2] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,-,2] => [1,2,4,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,-,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,-] => [1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,-,-] => [1,2,3,4] => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,3] => [1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,-,+,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[-,+,+,+,+] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[-,-,+,+,+] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[-,-,-,+,+] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[-,-,-,-,+] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[-,+,4,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[-,3,2,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[-,3,4,2,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[-,4,2,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(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)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[-,5,-,2,4] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(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)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[2,4,+,1,+] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[2,5,-,+,1] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(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)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[5,-,+,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[5,-,+,+,1] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,+,-,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[5,-,-,+,1] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
[5,-,+,-,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[5,-,4,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
[5,3,2,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(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
(load all 2 compositions to match this statistic)
Mapping
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Values
[+,+] => [1,2] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,3}
[-,+] => [2,1] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,3}
[+,-] => [1,2] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,3}
[-,-] => [1,2] => [2,1] => ([],2)
 => ? ∊ {1,1,1,1,3}
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
 => ? ∊ {1,1,1,1,3}
[+,+,+] => [1,2,3] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[-,+,+] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[+,-,+] => [1,3,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[+,+,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[-,-,+] => [3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[-,+,-] => [2,1,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[+,-,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[-,-,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[+,3,2] => [1,3,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[-,3,2] => [3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[2,1,+] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[2,1,-] => [2,1,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[2,3,1] => [3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[3,1,2] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[3,+,1] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[3,-,1] => [3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,2,2,2,2,4,4,4,4}
[+,+,+,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,+] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[+,-,+,+] => [1,3,4,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,+] => [1,2,4,3] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,+,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,+] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,+] => [2,4,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,+,-] => [2,3,1,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,+] => [1,4,2,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,+,-] => [1,3,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,+] => [4,1,2,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,+,-] => [3,1,2,4] => [3,4,2,1] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,-,-] => [2,1,3,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,+,4,3] => [1,2,4,3] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,+,4,3] => [2,4,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,-,4,3] => [1,4,2,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,-,4,3] => [4,1,2,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,+] => [1,3,4,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,+] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,2,-] => [1,3,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,2,-] => [3,1,2,4] => [3,4,2,1] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,3,4,2] => [1,4,2,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,3,4,2] => [4,1,2,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,2,3] => [1,3,4,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,2,3] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,+,2] => [1,3,4,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,+,2] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[+,4,-,2] => [1,4,2,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[-,4,-,2] => [4,1,2,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,+] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,1,-,+] => [2,4,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,+,-] => [2,3,1,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,+] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[3,+,1,+] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,1,2,3] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,1,+,2] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,+,1,3] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,+,+,1] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[-,+,+,+,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,1,+,+,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,1,2,+,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,+,1,+,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,1,2,3,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,1,+,2,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,+,1,3,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,+,+,1,+] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,2,3,4] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,2,+,3] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,+,2,4] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,+,+,2] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,+,1,3,4] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,+,1,+,3] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,+,+,1,4] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,+,+,+,1] => [2,3,4,5,1] => [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.