Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001540
Mapping
St001540: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 2
[-,+] => 0
[+,-] => 0
[-,-] => 2
[2,1] => 0
[+,+,+] => 3
[-,+,+] => 1
[+,-,+] => 1
[+,+,-] => 1
[-,-,+] => 1
[-,+,-] => 1
[+,-,-] => 1
[-,-,-] => 3
[+,3,2] => 1
[-,3,2] => 1
[2,1,+] => 1
[2,1,-] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 1
[3,-,1] => 1
[+,+,+,+] => 4
[-,+,+,+] => 2
[+,-,+,+] => 2
[+,+,-,+] => 2
[+,+,+,-] => 2
[-,-,+,+] => 0
[-,+,-,+] => 0
[-,+,+,-] => 0
[+,-,-,+] => 0
[+,-,+,-] => 0
[+,+,-,-] => 0
[-,-,-,+] => 2
[-,-,+,-] => 2
[-,+,-,-] => 2
[+,-,-,-] => 2
[-,-,-,-] => 4
[+,+,4,3] => 2
[-,+,4,3] => 0
[+,-,4,3] => 0
[-,-,4,3] => 2
[+,3,2,+] => 2
[-,3,2,+] => 0
[+,3,2,-] => 0
[-,3,2,-] => 2
[+,3,4,2] => 1
[-,3,4,2] => 1
[+,4,2,3] => 1
[-,4,2,3] => 1
[+,4,+,2] => 2
Description
Difference in positively decorated fixed points and negatively decorated fixed points.
Matching statistic: St001630
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 29% ●values known / values provided: 29%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => ([],2)
 => ([],1)
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[+,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => ([(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => ([(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {0,0,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => ([],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[3,-,1] => [3,2,1] => ([],3)
 => ([],1)
 => ? ∊ {0,0,1,1,1,1,3,3}
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[+,+,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,4,+,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,4,-,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[-,4,-,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,1,+,+] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,1,-,+] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,1,+,-] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,1,-,-] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,1,4,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,3,1,+] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,3,1,-] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[2,4,+,1] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[2,4,-,1] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,1,2,+] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,1,2,-] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[3,+,1,+] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,-,1,+] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,+,1,-] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,-,1,-] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,+,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,-,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[3,4,1,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[4,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[4,1,+,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[4,1,-,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[4,+,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,4}
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001629
(load all 2 compositions to match this statistic)
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => [2] => [1] => ? ∊ {0,0,0,2,2}
[-,+] => [2,1] => [1,1] => [2] => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2] => [1] => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2] => [1] => ? ∊ {0,0,0,2,2}
[2,1] => [1,2] => [2] => [1] => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [2,3,1] => [2,1] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [3,1,2] => [1,2] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [1,2,3] => [3] => [1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,-,1] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,+,+] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [2,3,4,1] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,3,4,2] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,4,3] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [3,4,1,2] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [2,4,1,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [2,3,1,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,4,2,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,3,2,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [4,1,2,3] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [3,1,2,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [2,3,1,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,3,2,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [3,1,2,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,2,4,3] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [2,4,1,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [2,3,1,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,3,2,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,+,2] => [3,2,1,4] => [1,1,2] => [2,1] => 0
[-,4,-,2] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,+,1,+] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,-,1,+] => [1,4,3,2] => [2,1,1] => [1,2] => 0
[4,-,+,1] => [3,1,4,2] => [1,2,1] => [1,1,1] => 1
[4,+,-,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[4,3,2,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[-,+,5,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[+,-,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[-,-,5,+,3] => [4,3,1,2,5] => [1,1,3] => [2,1] => 0
[-,+,5,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,-,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,-,5,-,3] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[-,3,5,+,2] => [4,2,1,3,5] => [1,1,3] => [2,1] => 0
[-,3,5,-,2] => [2,1,3,5,4] => [1,3,1] => [1,1,1] => 1
[+,4,+,2,+] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,4,+,2,+] => [3,2,5,1,4] => [1,2,2] => [1,2] => 0
[+,4,-,2,+] => [1,2,5,4,3] => [3,1,1] => [1,2] => 0
[-,4,-,2,+] => [2,5,1,4,3] => [2,2,1] => [2,1] => 0
[-,4,+,2,-] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,2,-] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,+,5,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,5,2] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,5,3,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,5,2,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[-,5,2,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[-,5,+,2,4] => [3,2,4,1,5] => [1,2,2] => [1,2] => 0
[-,5,-,2,4] => [2,4,1,5,3] => [2,2,1] => [2,1] => 0
[-,5,+,+,2] => [3,4,2,1,5] => [2,1,2] => [1,1,1] => 1
[+,5,-,+,2] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[+,5,+,-,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,-,+,2] => [4,2,1,5,3] => [1,1,2,1] => [2,1,1] => 1
[-,5,+,-,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[-,5,-,-,2] => [2,1,5,3,4] => [1,2,2] => [1,2] => 0
[-,5,4,2,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,5,4,3,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,4,3,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[2,1,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,1,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,4,+,1,+] => [3,1,5,2,4] => [1,2,2] => [1,2] => 0
[2,4,-,1,+] => [1,5,2,4,3] => [2,2,1] => [2,1] => 0
[2,5,1,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,5,1,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,+,1,4] => [3,1,4,2,5] => [1,2,2] => [1,2] => 0
[2,5,-,1,4] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[2,5,-,+,1] => [4,1,2,5,3] => [1,3,1] => [1,1,1] => 1
[2,5,+,-,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[2,5,4,1,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,4,3,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[3,+,1,+,+] => [2,1,4,5,3] => [1,3,1] => [1,1,1] => 1
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Matching statistic: St000260
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 26%●distinct values known / distinct values provided: 17%
Values
[+,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,1,+,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,-,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,+,-] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,4,+,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[2,4,-,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,1,+,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,1,-,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,+,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,-,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,+,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,-,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,3,5,+,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[2,3,5,-,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[2,4,5,3,1] => [2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[2,5,1,+,3] => [2,5,1,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000771
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 50%
Values
[+,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,1,+,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,-,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,+,-] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,4,+,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[2,4,-,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,+,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,-,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,-,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,-,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,3,5,+,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,3,5,-,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,4,5,3,1] => [2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,5,1,+,3] => [2,5,1,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Matching statistic: St000772
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 50%
Values
[+,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => [2] => ([],2)
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => [3] => ([],3)
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,+,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[-,4,-,2] => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,1,+,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,-,+] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,1,+,-] => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,4,4}
[2,4,+,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[2,4,-,1] => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,4,2,1] => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,+,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,1,-,2] => [4,1,3,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,-,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,+,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,-,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[+,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,+,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,+,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,-,5,-,3] => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,4,5,3,2] => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,2,+,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,2,-,3] => [1,5,2,4,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,+,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,-,+,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,+,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[-,5,-,-,2] => [1,5,3,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[+,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[-,5,4,3,2] => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,3,5,+,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,3,5,-,1] => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,4,5,3,1] => [2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,5,1,+,3] => [2,5,1,4,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $1$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$. The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
Matching statistic: St001603
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
[+,+] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => [1,1]
 => [1]
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,-,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
 => [1,1,1]
 => 1
[+,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[-,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 1
[2,5,1,+,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[3,1,5,+,2] => [3,1,5,4,2] => [2,2,1]
 => [2,1]
 => 1
[3,1,5,-,2] => [3,1,5,4,2] => [2,2,1]
 => [2,1]
 => 1
[3,+,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1
[3,-,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 1
[3,+,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1
[3,-,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 1
[3,+,5,+,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,-,5,+,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,+,5,-,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,-,5,-,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,5,1,+,2] => [3,5,1,4,2] => [2,2,1]
 => [2,1]
 => 1
[3,5,1,-,2] => [3,5,1,4,2] => [2,2,1]
 => [2,1]
 => 1
[3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 1
[3,5,2,+,1] => [3,5,2,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,5,2,-,1] => [3,5,2,4,1] => [2,2,1]
 => [2,1]
 => 1
[3,5,4,1,2] => [3,5,4,1,2] => [2,2,1]
 => [2,1]
 => 1
[3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,1,5,3,2] => [4,1,5,3,2] => [2,2,1]
 => [2,1]
 => 1
[4,+,1,5,3] => [4,2,1,5,3] => [2,2,1]
 => [2,1]
 => 1
[4,-,1,5,3] => [4,2,1,5,3] => [2,2,1]
 => [2,1]
 => 1
[4,+,5,1,3] => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 1
[4,-,5,1,3] => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 1
[4,+,5,3,1] => [4,2,5,3,1] => [2,2,1]
 => [2,1]
 => 1
[4,-,5,3,1] => [4,2,5,3,1] => [2,2,1]
 => [2,1]
 => 1
[4,3,1,5,2] => [4,3,1,5,2] => [2,2,1]
 => [2,1]
 => 1
[4,3,2,1,+] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,3,2,1,-] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,3,2,5,1] => [4,3,2,5,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,3,5,1,2] => [4,3,5,1,2] => [2,2,1]
 => [2,1]
 => 1
[4,3,5,2,1] => [4,3,5,2,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,5,1,3,2] => [4,5,1,3,2] => [2,2,1]
 => [2,1]
 => 1
[4,5,2,1,3] => [4,5,2,1,3] => [2,2,1]
 => [2,1]
 => 1
[4,5,2,3,1] => [4,5,2,3,1] => [2,2,1]
 => [2,1]
 => 1
[4,5,+,1,2] => [4,5,3,1,2] => [2,2,1]
 => [2,1]
 => 1
[4,5,-,1,2] => [4,5,3,1,2] => [2,2,1]
 => [2,1]
 => 1
[4,5,+,2,1] => [4,5,3,2,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[4,5,-,2,1] => [4,5,3,2,1] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,1,4,3,2] => [5,1,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 1
[5,+,1,+,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 1
[5,-,1,+,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 1
[5,+,1,-,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001604
Mapping
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 17%
Values
[+,+] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[-,+] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[+,-] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[-,-] => [1,2] => [2]
 => []
 => ? ∊ {0,0,0,2,2}
[2,1] => [2,1] => [1,1]
 => [1]
 => ? ∊ {0,0,0,2,2}
[+,+,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,+] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,+,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,-,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,-,-] => [1,2,3] => [3]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[-,3,2] => [1,3,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,+] => [2,1,3] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,1,-] => [2,1,3] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[2,3,1] => [2,3,1] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,1,2] => [3,1,2] => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,+,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[3,-,1] => [3,2,1] => [1,1,1]
 => [1,1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,3,3}
[+,+,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,+] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,+,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,-,-] => [1,2,3,4] => [4]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,+,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,+,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,-,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,-,4,3] => [1,2,4,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,+] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,+] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,2,-] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,2,-] => [1,3,2,4] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,3,4,2] => [1,3,4,2] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[-,4,2,3] => [1,4,2,3] => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[+,4,+,2] => [1,4,3,2] => [2,1,1]
 => [1,1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4}
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
 => [1,1,1]
 => 0
[+,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0
[-,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1]
 => [2,1]
 => 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0
[2,5,1,-,3] => [2,5,1,4,3] => [2,2,1]
 => [2,1]
 => 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
 => [2,1]
 => 0
[2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,2,1]
 => [2,1]
 => 0
[3,1,5,-,2] => [3,1,5,4,2] => [2,2,1]
 => [2,1]
 => 0
[3,+,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0
[3,-,1,5,4] => [3,2,1,5,4] => [2,2,1]
 => [2,1]
 => 0
[3,+,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0
[3,-,5,1,4] => [3,2,5,1,4] => [2,2,1]
 => [2,1]
 => 0
[3,+,5,+,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,-,5,+,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,+,5,-,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,-,5,-,1] => [3,2,5,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,2,1]
 => [2,1]
 => 0
[3,5,1,-,2] => [3,5,1,4,2] => [2,2,1]
 => [2,1]
 => 0
[3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
 => [2,1]
 => 0
[3,5,2,+,1] => [3,5,2,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,5,2,-,1] => [3,5,2,4,1] => [2,2,1]
 => [2,1]
 => 0
[3,5,4,1,2] => [3,5,4,1,2] => [2,2,1]
 => [2,1]
 => 0
[3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,1,5,3,2] => [4,1,5,3,2] => [2,2,1]
 => [2,1]
 => 0
[4,+,1,5,3] => [4,2,1,5,3] => [2,2,1]
 => [2,1]
 => 0
[4,-,1,5,3] => [4,2,1,5,3] => [2,2,1]
 => [2,1]
 => 0
[4,+,5,1,3] => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 0
[4,-,5,1,3] => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 0
[4,+,5,3,1] => [4,2,5,3,1] => [2,2,1]
 => [2,1]
 => 0
[4,-,5,3,1] => [4,2,5,3,1] => [2,2,1]
 => [2,1]
 => 0
[4,3,1,5,2] => [4,3,1,5,2] => [2,2,1]
 => [2,1]
 => 0
[4,3,2,1,+] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,3,2,1,-] => [4,3,2,1,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,3,2,5,1] => [4,3,2,5,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,3,5,1,2] => [4,3,5,1,2] => [2,2,1]
 => [2,1]
 => 0
[4,3,5,2,1] => [4,3,5,2,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,5,1,3,2] => [4,5,1,3,2] => [2,2,1]
 => [2,1]
 => 0
[4,5,2,1,3] => [4,5,2,1,3] => [2,2,1]
 => [2,1]
 => 0
[4,5,2,3,1] => [4,5,2,3,1] => [2,2,1]
 => [2,1]
 => 0
[4,5,+,1,2] => [4,5,3,1,2] => [2,2,1]
 => [2,1]
 => 0
[4,5,-,1,2] => [4,5,3,1,2] => [2,2,1]
 => [2,1]
 => 0
[4,5,+,2,1] => [4,5,3,2,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[4,5,-,2,1] => [4,5,3,2,1] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,1,4,3,2] => [5,1,4,3,2] => [2,1,1,1]
 => [1,1,1]
 => 0
[5,+,1,+,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 0
[5,-,1,+,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 0
[5,+,1,-,3] => [5,2,1,4,3] => [2,2,1]
 => [2,1]
 => 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.