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Matching statistic: St001547
St001547: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 0
[-,+] => 2
[+,-] => 4
[-,-] => 6
[2,1] => 3
[+,+,+] => 0
[-,+,+] => 3
[+,-,+] => 6
[+,+,-] => 9
[-,-,+] => 9
[-,+,-] => 12
[+,-,-] => 15
[-,-,-] => 18
[+,3,2] => 7
[-,3,2] => 10
[2,1,+] => 4
[2,1,-] => 13
[2,3,1] => 6
[3,1,2] => 12
[3,+,1] => 7
[3,-,1] => 13
[+,+,+,+] => 0
[-,+,+,+] => 4
[+,-,+,+] => 8
[+,+,-,+] => 12
[+,+,+,-] => 16
[-,-,+,+] => 12
[-,+,-,+] => 16
[-,+,+,-] => 20
[+,-,-,+] => 20
[+,-,+,-] => 24
[+,+,-,-] => 28
[-,-,-,+] => 24
[-,-,+,-] => 28
[-,+,-,-] => 32
[+,-,-,-] => 36
[-,-,-,-] => 40
[+,+,4,3] => 13
[-,+,4,3] => 17
[+,-,4,3] => 21
[-,-,4,3] => 25
[+,3,2,+] => 9
[-,3,2,+] => 13
[+,3,2,-] => 25
[-,3,2,-] => 29
[+,3,4,2] => 11
[-,3,4,2] => 15
[+,4,2,3] => 23
[-,4,2,3] => 27
[+,4,+,2] => 12
Description
The sum of all indices from every element of the Grassmann necklace.
Here, we use Postnikov's map (p.59) from decorated permutations to Grassmann necklaces.
Matching statistic: St000467
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 26%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 26%
Values
[+,+] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,3,4,6}
[-,+] => [2,1] => [2,1] => ([(0,1)],2)
=> 2
[+,-] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,3,4,6}
[-,-] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,3,4,6}
[2,1] => [1,2] => [1,2] => ([],2)
=> ? ∊ {0,3,4,6}
[+,+,+] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[-,+,+] => [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
=> 10
[+,-,+] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[+,+,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[-,-,+] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 6
[-,+,-] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[+,-,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[-,-,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[+,3,2] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[-,3,2] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[2,1,+] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[2,1,-] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[2,3,1] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[3,1,2] => [1,2,3] => [1,2,3] => ([],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[3,+,1] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[3,-,1] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,3,4,6,7,7,9,9,12,12,13,13,15,18}
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,+,+,+] => [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 24
[+,-,+,+] => [1,3,4,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,+,-,+] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,-,+,+] => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 30
[-,+,-,+] => [2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 16
[-,+,+,-] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,-,-,+] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,-,+,-] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,-,-,+] => [4,1,2,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 12
[-,-,+,-] => [3,1,2,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,+,-,-] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,+,4,3] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,+,4,3] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,-,4,3] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,-,4,3] => [3,1,2,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,3,2,+] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,3,2,+] => [2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 16
[+,3,2,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,3,2,-] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,3,4,2] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,3,4,2] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,4,2,3] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,4,2,3] => [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,4,+,2] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,4,+,2] => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[+,4,-,2] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[-,4,-,2] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[2,1,+,+] => [1,3,4,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[2,1,-,+] => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[2,1,+,-] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[2,1,-,-] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[2,1,4,3] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,4,5,7,8,8,9,10,11,11,11,12,12,13,13,13,15,15,16,16,17,17,17,18,19,19,20,20,21,21,21,21,21,21,22,23,23,23,23,24,24,24,25,25,25,27,28,28,28,29,31,31,31,32,32,33,33,36,40}
[4,-,+,1] => [3,1,4,2] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 20
[-,+,+,+,+] => [2,3,4,5,1] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 44
[-,-,+,+,+] => [3,4,5,1,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[-,+,-,+,+] => [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 56
[-,+,+,-,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[-,-,-,+,+] => [4,5,1,2,3] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[-,-,+,-,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 52
[-,+,-,-,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
[-,-,-,-,+] => [5,1,2,3,4] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 20
[-,+,4,3,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[-,-,4,3,+] => [3,5,1,2,4] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 52
[-,3,2,+,+] => [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 56
[-,3,2,-,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
[-,3,4,2,+] => [2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
[-,4,2,3,+] => [2,3,5,1,4] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[-,4,+,2,+] => [3,2,5,1,4] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 42
[-,4,-,2,+] => [2,5,1,4,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 28
[-,5,-,2,4] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 36
[-,5,-,+,2] => [4,2,1,5,3] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 46
[2,4,+,1,+] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 28
[2,5,-,+,1] => [4,1,2,5,3] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 32
[4,-,+,1,+] => [3,1,5,4,2] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 32
[5,-,+,1,4] => [3,1,4,5,2] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 40
[5,-,+,+,1] => [3,4,1,5,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 70
[5,+,-,+,1] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 36
[5,-,-,+,1] => [4,1,5,2,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 52
[5,-,+,-,1] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 28
[5,-,4,3,1] => [3,1,5,2,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 28
[5,3,2,+,1] => [2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 36
Description
The hyper-Wiener index of a connected graph.
This is
$$
\sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2.
$$
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