Values
=>
Cc0020;cc-rep
([],1)=>1
([],2)=>1
([(0,1)],2)=>1
([],3)=>2
([(1,2)],3)=>4
([(0,2),(1,2)],3)=>2
([(0,1),(0,2),(1,2)],3)=>1
([],4)=>3
([(2,3)],4)=>3
([(1,3),(2,3)],4)=>9
([(0,3),(1,3),(2,3)],4)=>3
([(0,3),(1,2)],4)=>3
([(0,3),(1,2),(2,3)],4)=>3
([(1,2),(1,3),(2,3)],4)=>9
([(0,3),(1,2),(1,3),(2,3)],4)=>3
([(0,2),(0,3),(1,2),(1,3)],4)=>2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1
([],5)=>4
([(3,4)],5)=>8
([(2,4),(3,4)],5)=>12
([(1,4),(2,4),(3,4)],5)=>16
([(0,4),(1,4),(2,4),(3,4)],5)=>4
([(1,4),(2,3)],5)=>8
([(1,4),(2,3),(3,4)],5)=>16
([(0,1),(2,4),(3,4)],5)=>24
([(2,3),(2,4),(3,4)],5)=>12
([(0,4),(1,4),(2,3),(3,4)],5)=>4
([(1,4),(2,3),(2,4),(3,4)],5)=>16
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(1,3),(1,4),(2,3),(2,4)],5)=>32
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>8
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>32
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>6
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,4),(1,3),(2,3),(2,4)],5)=>4
([(0,1),(2,3),(2,4),(3,4)],5)=>24
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>24
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>15
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>8
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>16
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([],6)=>5
([(4,5)],6)=>5
([(3,5),(4,5)],6)=>5
([(2,5),(3,5),(4,5)],6)=>10
([(1,5),(2,5),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>5
([(2,5),(3,4)],6)=>5
([(2,5),(3,4),(4,5)],6)=>10
([(1,2),(3,5),(4,5)],6)=>5
([(3,4),(3,5),(4,5)],6)=>5
([(1,5),(2,5),(3,4),(4,5)],6)=>25
([(0,1),(2,5),(3,5),(4,5)],6)=>10
([(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>5
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(2,4),(2,5),(3,4),(3,5)],6)=>20
([(0,5),(1,5),(2,4),(3,4)],6)=>5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>20
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>5
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>10
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>25
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>15
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,5),(1,4),(2,3)],6)=>5
([(1,5),(2,4),(3,4),(3,5)],6)=>25
([(0,1),(2,5),(3,4),(4,5)],6)=>10
([(1,2),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>5
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>25
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>25
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>25
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>10
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>125
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>30
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>75
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>20
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>5
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>10
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>20
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>10
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>10
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>924
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>2184
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>15
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>84
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>840
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>15
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>15
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>25
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>15
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>25
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>60
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>1092
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>75
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>10032
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>10
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>75
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>60
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>15
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>132
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>60
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>24
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>15
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>24
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>168
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>336
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>24
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>168
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>24
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>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)=>6
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>5
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>10
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>5
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>132
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1092
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>15
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>60
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>84
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>420
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>840
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>462
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>120
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>15
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>462
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>24
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>420
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>30
([(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)=>6
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>24
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>84
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>25
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>12
([(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)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>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)],6)=>2
([(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)=>2
([(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)=>2
([(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)=>1
([],7)=>6
([(5,6)],7)=>12
([(4,6),(5,6)],7)=>18
([(3,6),(4,6),(5,6)],7)=>24
([(2,6),(3,6),(4,6),(5,6)],7)=>30
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>36
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(3,6),(4,5)],7)=>12
([(3,6),(4,5),(5,6)],7)=>24
([(2,3),(4,6),(5,6)],7)=>36
([(4,5),(4,6),(5,6)],7)=>18
([(2,6),(3,6),(4,5),(5,6)],7)=>30
([(1,2),(3,6),(4,6),(5,6)],7)=>24
([(3,6),(4,5),(4,6),(5,6)],7)=>24
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>36
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>60
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>30
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>6
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(3,5),(3,6),(4,5),(4,6)],7)=>48
([(1,6),(2,6),(3,5),(4,5)],7)=>18
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>60
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>36
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>72
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>48
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>30
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>36
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>72
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>6
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>36
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>6
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>12
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>6
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>12
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>90
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>72
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>6
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>108
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>12
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>90
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>6
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>18
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>12
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>432
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>18
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>72
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>60
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(1,6),(2,5),(3,4)],7)=>12
([(2,6),(3,5),(4,5),(4,6)],7)=>30
([(1,2),(3,6),(4,5),(5,6)],7)=>24
([(0,3),(1,2),(4,6),(5,6)],7)=>36
([(2,3),(4,5),(4,6),(5,6)],7)=>36
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>36
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>60
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>30
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>24
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>6
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>36
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>30
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>36
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>6
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>180
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>72
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>450
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>216
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>60
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>36
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>540
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>90
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>36
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>48
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>18
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>72
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>60
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>36
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>48
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>60
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>36
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>12
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>72
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>72
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>12
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>72
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>24
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>6
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>72
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>30
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>12
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>4752
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>18
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>11232
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>108
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>12
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>180
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>18
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>12
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>180
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>18
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>108
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>90
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>72
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>72
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>432
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>108
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>90
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>108
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>30
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>36
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>432
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>5616
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>540
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>361152
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>72
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>540
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>12
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>108
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>4752
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>432
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>18
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>6
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>6
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>864
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>18
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>108
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>864
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>18
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>30
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>1728
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>18
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>864
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>216
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>216
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>864
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>216
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>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)=>216
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>60
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>6
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>60
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>6
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>12
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>12
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>18
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>72
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>36
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>24
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>72
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>60
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>4752
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>5616
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>108
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>432
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>90
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>864
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>2376
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>864
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>108
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>2376
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>864
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>432
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>216
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>18
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>864
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(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)=>216
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>30
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>36
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>432
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>216
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>216
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>432
([(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)=>216
([(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)=>216
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>72
([(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)=>72
([(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
([(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)=>36
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Description
The order of toric promotion on the set of labellings of a graph.
In the context of toric promotion, a labelling of a graph $(V, E)$ with $n=|V|$ vertices is a bijection $\sigma: V \to [n]$. In particular, any graph has $n!$ labellings.
In the context of toric promotion, a labelling of a graph $(V, E)$ with $n=|V|$ vertices is a bijection $\sigma: V \to [n]$. In particular, any graph has $n!$ labellings.
References
[1] Defant, C. Toric Promotion arXiv:2112.06843
Code
from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
def toggle_labelling(G, pi, i, j):
if G.has_edge(pi.index(i), pi.index(j)):
return pi
sigma = [j if e == i else i if e == j else e for e in pi]
return Permutation(sigma)
def toric_promotion_labelling(G, pi):
n = G.num_verts()
assert set(G.vertices()) == set(range(n))
for i in range(1, n):
pi = toggle_labelling(G, pi, i, i+1)
return toggle_labelling(G, pi, n, 1)
def toric_promotion_labelling_orbits(G):
G = G.canonical_label().copy(immutable=True)
return toric_promotion_labelling_orbits_aux(G)
@cached_function
def toric_promotion_labelling_orbits_aux(G):
n = G.num_verts()
return orbit_decomposition(Permutations(n),
lambda pi: toric_promotion_labelling(G, pi))
def statistic(G):
return lcm(len(o) for o in toric_promotion_labelling_orbits(G))
Created
Aug 18, 2023 at 22:21 by Martin Rubey
Updated
Aug 18, 2023 at 22:21 by Martin Rubey
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