Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000467
Mapping
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+] => [1] => [1] => ([],1)
 => 0
[-] => [1] => [1] => ([],1)
 => 0
[-,+] => [2,1] => [2,1] => ([(0,1)],2)
 => 2
[-,+,+] => [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
 => 10
[-,-,+] => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 6
[-,+,+,+] => [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 24
[-,-,+,+] => [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
[-,-,-,+] => [4,1,2,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 12
[-,3,2,+] => [2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 16
[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
[-,+,+,+,+,+] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 70
[-,-,+,+,+,+] => [3,4,5,6,1,2] => [5,1,3,6,2,4] => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 68
[-,+,-,+,+,+] => [2,4,5,6,1,3] => [6,3,5,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 50
[-,+,+,-,+,+] => [2,3,5,6,1,4] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 88
[-,+,+,+,-,+] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 54
[-,-,-,+,+,+] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 84
[-,-,+,-,+,+] => [3,5,6,1,2,4] => [5,2,6,4,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 50
[-,-,+,+,-,+] => [3,4,6,1,2,5] => [6,5,2,4,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 42
[-,+,-,-,+,+] => [2,5,6,1,3,4] => [6,4,1,2,5,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 54
[-,+,-,+,-,+] => [2,4,6,1,3,5] => [4,1,2,6,5,3] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 90
[-,+,+,-,-,+] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 42
Description
The hyper-Wiener index of a connected graph. This is ∑{u,v}⊆Vd(u,v)+d(u,v)2.