searching the database
Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000269
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> 1
([],2)
=> 1
([(0,1)],2)
=> 2
([],3)
=> 1
([(1,2)],3)
=> 2
([(0,2),(1,2)],3)
=> 4
([(0,1),(0,2),(1,2)],3)
=> 6
([],4)
=> 1
([(2,3)],4)
=> 2
([(1,3),(2,3)],4)
=> 4
([(0,3),(1,3),(2,3)],4)
=> 8
([(0,3),(1,2)],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> 8
([(1,2),(1,3),(2,3)],4)
=> 6
([(0,3),(1,2),(1,3),(2,3)],4)
=> 12
([(0,2),(0,3),(1,2),(1,3)],4)
=> 14
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 18
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 24
([],5)
=> 1
([(3,4)],5)
=> 2
([(2,4),(3,4)],5)
=> 4
([(1,4),(2,4),(3,4)],5)
=> 8
([(0,4),(1,4),(2,4),(3,4)],5)
=> 16
([(1,4),(2,3)],5)
=> 4
([(1,4),(2,3),(3,4)],5)
=> 8
([(0,1),(2,4),(3,4)],5)
=> 8
([(2,3),(2,4),(3,4)],5)
=> 6
([(0,4),(1,4),(2,3),(3,4)],5)
=> 16
([(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([(1,3),(1,4),(2,3),(2,4)],5)
=> 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 28
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 46
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 54
([(0,4),(1,3),(2,3),(2,4)],5)
=> 16
([(0,1),(2,3),(2,4),(3,4)],5)
=> 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 36
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 42
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 54
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 36
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 60
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 78
Description
The number of acyclic orientations of a graph.
Matching statistic: St000948
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([(0,1)],2)
=> ([],1)
=> 1
([],2)
=> ([(0,2),(1,2)],3)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 14
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 18
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 16
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 4
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 8
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 16
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 28
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 46
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(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)
=> 54
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 16
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 42
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(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)
=> 54
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 60
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 78
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {24,24,28,36,36,48,48,72,96}
Description
The chromatic discriminant of a graph.
The chromatic discriminant $\alpha(G)$ is the coefficient of the linear term of the chromatic polynomial $\chi(G,q)$.
According to [1], it equals the cardinality of any of the following sets:
(1) Acyclic orientations of G with unique sink at $q$,
(2) Maximum $G$-parking functions relative to $q$,
(3) Minimal $q$-critical states,
(4) Spanning trees of G without broken circuits,
(5) Conjugacy classes of Coxeter elements in the Coxeter group associated to $G$,
(6) Multilinear Lyndon heaps on $G$.
In addition, $\alpha(G)$ is also equal to the the dimension of the root space corresponding to the sum of all simple roots in the Kac-Moody Lie algebra associated to the graph.
Matching statistic: St001475
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
([],1)
=> ([(0,1)],2)
=> ([],1)
=> 1
([],2)
=> ([(0,2),(1,2)],3)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 14
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 18
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 16
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 4
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 8
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 16
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 28
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 46
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(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)
=> 54
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 16
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 42
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(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)
=> 54
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 36
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 60
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 78
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {186,192,204,216,234,240,240,240,258,288,288,312,312,330,336,360,384,408,426,480,504,600,720}
Description
The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0).
Matching statistic: St001070
Values
([],1)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([],2)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 8
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 8
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 12
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 14
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 18
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 28
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 46
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 54
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 42
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 54
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 60
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 78
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 96
([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
Description
The absolute value of the derivative of the chromatic polynomial of the graph at 1.
This is closely related to Crapo's beta invariant, the only difference being the value for the graphs without edges.
Matching statistic: St001071
Values
([],1)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 1
([],2)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 6
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 8
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 8
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 12
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 14
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 18
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 24
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 4
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 8
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 6
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 14
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 28
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 46
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 54
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 16
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 12
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 42
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 54
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 36
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 24
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 60
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 78
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 96
([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,2,4,4,6,8,8,8,8,12,12,14,16,16,16,16,16,16,18,24,24,24,24,24,24,28,28,30,32,32,32,32,32,32,36,36,36,36,36,42,46,48,48,48,48,48,48,48,48,48,54,54,56,56,56,56,60,60,62,72,72,72,72,72,72,72,72,72,72,72,78,84,84,84,84,90,92,92,96,96,96,96,98,102,108,108,108,108,108,108,108,120,120,120,120,126,126,126,126,132,138,144,144,144,144,144,146,152,156,156,162,162,162,162,162,168,180,180,180,186,192,192,192,198,204,216,216,216,216,230,234,234,240,240,240,252,252,258,276,288,288,288,312,312,330,330,336,360,384,384,408,426,480,504,600,720}
Description
The beta invariant of the graph.
The beta invariant was introduced by Crapo [1] for matroids. For graphs with $n$ vertices the beta invariant is
$$\beta(G) = (-1)^{n-c}\sum_{S\subseteq E} (-1)^{|S|} (n-c(S)),$$
where $c(S)$ is the number of connected components of the subgraph of $G$ with edge set $S$.
For graphs with at least one edge the beta invariant equals the absolute value of the derivative of the chromatic polynomial at $1$. [2]
The beta invariant also coincides with the coefficient of the monomial $x$, and also with the coefficient of the monomial $y$, of the Tutte polynomial.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!