Identifier
-
Mp00307:
Posets
—promotion cycle type⟶
Integer partitions
St001251: Integer partitions ⟶ ℤ
Values
([],1) => [1] => 0
([],2) => [2] => 1
([(0,1)],2) => [1] => 0
([],3) => [3,3] => 2
([(1,2)],3) => [3] => 1
([(0,1),(0,2)],3) => [2] => 1
([(0,2),(2,1)],3) => [1] => 0
([(0,2),(1,2)],3) => [2] => 1
([],4) => [4,4,4,4,4,4] => 0
([(2,3)],4) => [4,4,4] => 0
([(1,2),(1,3)],4) => [8] => 1
([(0,1),(0,2),(0,3)],4) => [3,3] => 2
([(0,2),(0,3),(3,1)],4) => [3] => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 1
([(1,2),(2,3)],4) => [4] => 0
([(0,3),(3,1),(3,2)],4) => [2] => 1
([(1,3),(2,3)],4) => [8] => 1
([(0,3),(1,3),(3,2)],4) => [2] => 1
([(0,3),(1,3),(2,3)],4) => [3,3] => 2
([(0,3),(1,2)],4) => [4,2] => 1
([(0,3),(1,2),(1,3)],4) => [3,2] => 2
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => 2
([(0,3),(2,1),(3,2)],4) => [1] => 0
([(0,3),(1,2),(2,3)],4) => [3] => 1
([],5) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(3,4)],5) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(2,3),(2,4)],5) => [10,10,10,10] => 0
([(1,2),(1,3),(1,4)],5) => [15,15] => 2
([(0,1),(0,2),(0,3),(0,4)],5) => [4,4,4,4,4,4] => 0
([(0,2),(0,3),(0,4),(4,1)],5) => [4,4,4] => 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => [8] => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => 2
([(1,3),(1,4),(4,2)],5) => [15] => 1
([(0,3),(0,4),(4,1),(4,2)],5) => [8] => 1
([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => 1
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => 2
([(2,3),(3,4)],5) => [5,5,5,5] => 4
([(1,4),(4,2),(4,3)],5) => [5,5] => 2
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => 2
([(2,4),(3,4)],5) => [10,10,10,10] => 0
([(1,4),(2,4),(4,3)],5) => [5,5] => 2
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => 2
([(1,4),(2,4),(3,4)],5) => [15,15] => 2
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 2
([(0,4),(1,4),(2,4),(3,4)],5) => [4,4,4,4,4,4] => 0
([(0,4),(1,4),(2,3)],5) => [10,10] => 0
([(0,4),(1,3),(2,3),(2,4)],5) => [12,4] => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [14] => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [6,6] => 2
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 1
([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 1
([(0,4),(1,4),(2,3),(2,4)],5) => [10,4,4] => 0
([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 0
([(1,4),(2,3)],5) => [5,5,5,5,5,5] => 6
([(1,4),(2,3),(2,4)],5) => [15,5,5] => 3
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 2
([(1,3),(1,4),(2,3),(2,4)],5) => [5,5,5,5] => 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => 2
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => 0
([(0,4),(1,2),(1,3)],5) => [10,10] => 0
([(0,4),(1,2),(1,3),(1,4)],5) => [10,4,4] => 0
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 0
([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [8] => 1
([(0,3),(0,4),(1,2),(1,4)],5) => [12,4] => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [14] => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [6,6] => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => 2
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => 1
([(1,4),(3,2),(4,3)],5) => [5] => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => 1
([(1,4),(2,3),(3,4)],5) => [15] => 1
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 1
([(0,3),(1,4),(4,2)],5) => [5,5] => 2
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => 1
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => 0
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 0
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 1
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => 1
([],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 120
([(4,5)],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 60
([(3,4),(3,5)],6) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(2,3),(2,4),(2,5)],6) => [18,18,18,18,18,18,18,18,18,18] => 10
([(1,2),(1,3),(1,4),(1,5)],6) => [24,24,24,24,24,24] => 6
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => [10,10,10,10] => 0
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => [15,15] => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => [4,4,4,4,4,4] => 0
([(1,3),(1,4),(1,5),(5,2)],6) => [24,24,24] => 3
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => [10,10,10,10] => 0
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => [48] => 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [18,18] => 2
>>> Load all 775 entries. <<<([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => [10,10] => 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => [12,4] => 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [14] => 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6,6] => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => [10,4,4] => 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => [8] => 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,5] => 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => [5,5,5,5,5,5] => 6
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => [15,5,5] => 3
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => [5,5,5,5] => 4
([(2,3),(2,4),(4,5)],6) => [18,18,18,18,18] => 5
([(1,4),(1,5),(5,2),(5,3)],6) => [48] => 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => [15,15] => 2
([(2,3),(2,4),(3,5),(4,5)],6) => [6,6,6,6,6,6,6,6,6,6] => 10
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [12] => 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => 2
([(1,4),(1,5),(4,3),(5,2)],6) => [24,12] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => 0
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => [10,10] => 0
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => [10,4,4] => 0
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => [12,4] => 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => [14] => 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [6,6] => 2
([(3,4),(4,5)],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(2,3),(3,4),(3,5)],6) => [6,6,6,6,6,6,6,6,6,6] => 10
([(1,5),(5,2),(5,3),(5,4)],6) => [18,18] => 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => [4,4,4,4,4,4] => 0
([(2,3),(3,5),(5,4)],6) => [6,6,6,6,6] => 5
([(1,4),(4,5),(5,2),(5,3)],6) => [12] => 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => 2
([(3,5),(4,5)],6) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(2,5),(3,5),(5,4)],6) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [6,6] => 2
([(2,5),(3,5),(4,5)],6) => [18,18,18,18,18,18,18,18,18,18] => 10
([(1,5),(2,5),(3,5),(5,4)],6) => [18,18] => 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [6,6] => 2
([(1,5),(2,5),(3,5),(4,5)],6) => [24,24,24,24,24,24] => 6
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => [4,4,4,4,4,4] => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(0,5),(1,5),(2,5),(3,4)],6) => [18,18,18,18,9,9] => 6
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => [15,15] => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(1,5),(2,5),(3,4)],6) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [12,4] => 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [14] => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => [3,3,3,3,3,3] => 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6,6] => 2
([(1,5),(2,5),(3,4),(5,3)],6) => [12] => 1
([(1,5),(2,4),(3,4),(4,5)],6) => [48] => 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 1
([(0,5),(1,5),(2,3),(5,4)],6) => [6,6,6,6,3,3] => 6
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => [10,4,4] => 0
([(0,5),(1,5),(2,3),(2,4)],6) => [12,12,12,12,12,12,4,4] => 6
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => 2
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [8,8] => 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,5] => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => 1
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => [15] => 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => [8] => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [10,10,10,10] => 0
([(1,5),(2,5),(3,4),(4,5)],6) => [24,24,24] => 3
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 0
([(0,5),(1,5),(2,3),(3,4)],6) => [12,12,12,4] => 3
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [10,10] => 0
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => [14] => 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [8] => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5,5,5,5] => 4
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,5] => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => 2
([(0,5),(1,5),(2,4),(3,4)],6) => [12,12,12,12,12,12,4,4] => 6
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [10,10,10,10] => 0
([(2,5),(3,4)],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 30
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => [8,4,2] => 2
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [6,2,2] => 3
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => 2
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => [14,2] => 2
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => [10,2] => 1
([(2,4),(2,5),(3,4),(3,5)],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => [8,8] => 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,4,2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [6,2,2] => 3
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => 0
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [5,5,5,5] => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => [4,4,4,4,4,4] => 0
([(1,5),(2,3),(2,4)],6) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [10,4,4] => 0
([(0,5),(1,2),(1,3),(1,4)],6) => [18,18,18,18,9,9] => 6
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => [5,5,5,5] => 4
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => [15] => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => [4,4,4] => 0
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [15,15] => 2
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [3,3,3,3,3,3] => 6
([(1,3),(1,5),(4,2),(5,4)],6) => [24] => 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,5] => 2
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 2
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 2
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => 2
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => [14] => 1
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => [18] => 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [48] => 1
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [8] => 1
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => [4,4,3] => 1
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,4,3] => 1
([(0,4),(1,3),(1,5),(5,2)],6) => [18,18,9] => 3
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => [15] => 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => 0
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => [6,6,6,6,3,3] => 6
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [10,10] => 0
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,5] => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => [4,4,4,4,4,4] => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => [8,8] => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [6,6] => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [14] => 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => [13,2] => 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => [8,3] => 2
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => [5,3] => 2
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => [8,3,2] => 3
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => [12,4] => 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => [6,4,3] => 2
([(0,4),(0,5),(1,2),(1,3)],6) => [12,12,12,12,12,12,4,4] => 6
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [6] => 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => [7] => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [8,8] => 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => [9,3] => 2
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [3,3,3] => 3
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6] => 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => [13,2] => 1
([(0,5),(1,3),(1,4),(5,2)],6) => [12,12,12,4] => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => 1
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => [8] => 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => [8,3] => 2
([(2,5),(3,4),(4,5)],6) => [18,18,18,18,18] => 5
([(1,5),(2,3),(3,5),(5,4)],6) => [18] => 1
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [6] => 1
([(1,3),(2,4),(4,5)],6) => [6,6,6,6,6,6,6,6,6,6] => 10
([(1,5),(4,3),(5,2),(5,4)],6) => [18] => 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [4,3,3] => 2
([(0,4),(1,5),(5,2),(5,3)],6) => [6,6,6,6,3,3] => 6
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => [4,4,4] => 0
([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => 1
([(1,4),(2,3),(3,5),(4,5)],6) => [24,12] => 2
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => 1
([(0,5),(1,4),(4,2),(5,3)],6) => [6,6,6,2] => 4
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [4] => 0
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => [14,2] => 2
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => 2
([(1,5),(2,3),(3,4),(4,5)],6) => [24] => 1
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [12] => 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 0
([(0,5),(1,4),(2,3)],6) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 16
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => [6,5,3] => 3
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,4] => 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => [7] => 0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [15,5,5] => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [5,4] => 1
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => [6,5,3] => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [4,4] => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [3,2] => 2
([(0,5),(1,3),(4,2),(5,4)],6) => [6,6,3] => 3
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [4,2] => 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => [9,3] => 2
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => [7] => 0
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [5,4] => 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => 0
([(0,5),(1,3),(2,4),(4,5)],6) => [18,18,9] => 3
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 1
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => 1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5,5,5,5,5,5] => 6
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 120
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 60
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => [18,18,18,18,18,18,18,18,18,18] => 10
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => [24,24,24,24,24,24] => 6
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => [4,4,4,4,4,4] => 0
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => [18,18,18,18,9,9] => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => [15,15] => 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => [18,18] => 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [10,10,10,10] => 0
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => [48] => 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 30
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => [18,18,18,18,18,18,18,18,18,18] => 10
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => [6,6] => 2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => [3,3,3,3,3,3] => 6
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [6,6] => 2
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => [14] => 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [12,4] => 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [8,8] => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => [8] => 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => [6,6,6,6,3,3] => 6
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [5,5,5,5] => 4
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 16
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => [24,24,24,24,24,24] => 6
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => [6,6] => 2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => [8,8] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => 2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [4,4,2,2] => 2
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [6,2,2] => 3
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => 4
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => [18,18,18,18,9,9] => 6
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => [4,4,4,4,4,4] => 0
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => [8,8] => 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [6,6] => 2
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => [6] => 1
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => [4,4,4,4,4,4] => 0
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 24
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 120
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => [4,4,4,4,4,4] => 0
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => [24,24,24,24,24,24] => 6
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 60
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => [3,3,3,3,3,3] => 6
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => [11,11,11,11,11,11] => 6
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => [6,6] => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => 2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => [15,15] => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => [18,18,18,18,9,9] => 6
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => [6,6,6,6,6] => 5
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => [12] => 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [3,3] => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => [18,18] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6,6] => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => [18,18,18,18,18,18,18,18,18,18] => 10
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => [6,6] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 20
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => [12,4] => 1
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => [9,9,9,9,3,3] => 6
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [6,6,6,6] => 4
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => [6,6] => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => [3,3,3,3,3,3] => 6
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => [14] => 1
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => [8,8] => 2
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => [4,4,4,4,4,4] => 0
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => [10,4,4] => 0
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => [24] => 1
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => [8,8] => 2
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => [6,6] => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => [24,12] => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => [48] => 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => [5,5,5,5,5,5] => 6
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [24,24,24] => 3
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => [10,10,10,10] => 0
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [18,18,18,18,18,18,18,18,18,18] => 10
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => [10,10,10,10] => 0
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => [6] => 1
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [8,8] => 2
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => [48] => 1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => [12,4] => 1
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => [6,6,6,6,3,3] => 6
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => [5,5] => 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => [10,4,4] => 0
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => [7] => 0
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => [18,18,18,18,18] => 5
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => [48] => 1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => [15,15] => 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => 2
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => [12] => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => 2
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => [18,18] => 2
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => [24,12] => 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => [10,10] => 0
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => [4,4,4,4,4,4] => 0
([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [7,7] => 0
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => [10,10] => 0
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [4,4] => 0
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => 2
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => [10,10,10,10] => 0
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [10,10,10,10] => 0
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [15,15] => 2
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => [18,18] => 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [4,4,4,4,4,4] => 0
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 1
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => [7,7] => 0
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => 1
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => [5,5,5,5] => 4
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => 1
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => [12,12,12,4] => 3
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => [17] => 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [8] => 1
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => 2
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => [10,10,10,10] => 0
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => [8,8] => 2
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [4,4,2,2] => 2
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 1
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => [48] => 1
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => [10,10,10] => 0
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => [22] => 0
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [6,2,2] => 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => [10,10] => 0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [2,2,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => [10,10] => 0
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [4,4,2,2] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [6,2,2] => 3
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => 4
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => [8,8] => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => [22] => 0
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 0
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => [24,24,24] => 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 30
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [12] => 1
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => [6,6,6,6,3,3] => 6
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => [6] => 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => [18] => 1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6] => 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => [18,18,18,18,18] => 5
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => [9,9,9,9,3,3] => 6
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [6,2,2] => 3
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => [5,4] => 1
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => [11,3,3] => 3
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => [10,4,4] => 0
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => [10,10,10,10] => 0
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => [6,6,6,6] => 4
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => [10,10] => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => [10,4,4] => 0
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => [10,6] => 1
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => [14] => 1
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => [10,4,4] => 0
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => [5,5,5,5] => 4
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => [10,10] => 0
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [2,2,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => [14] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => [6,6] => 2
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => [48] => 1
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [10,10,10,10] => 0
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [4,4,2,2] => 2
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => [8,8] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,4,4,4,4,4] => 0
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => [10] => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => 2
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => [6] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [4,4] => 0
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [5,5,5,5] => 4
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => [24] => 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [14] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => [10,10,10,10] => 0
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => [10,10] => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [6,6] => 2
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => [11,11,11,11,11,11] => 6
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => [10,4,4] => 0
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 20
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => [18,18,18,18,18] => 5
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => [24,24,24] => 3
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => [24,24,24,24,24,24] => 6
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => [18] => 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => [4,4,4] => 0
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => [15,15] => 2
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,1),(5,2)],7) => [18,18,9] => 3
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => [15] => 1
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => [15,5,5] => 3
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [11,11,11,11,11,11] => 6
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => [5,5] => 2
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => [48] => 1
([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => [18,18,18,18,18] => 5
([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7) => [24] => 1
([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => [5,5,5,5] => 4
([(0,2),(0,3),(0,5),(2,6),(3,6),(4,1),(5,4)],7) => [12,12,12,4] => 3
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => [10,4,4] => 0
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => [10,10] => 0
([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(5,6)],7) => [18,18,18,18,9,9] => 6
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [3,3] => 2
([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => [18,18] => 2
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7) => [12] => 1
([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => [24] => 1
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,3,3] => 6
([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => [6,6,6,6,6] => 5
([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7) => [18,18] => 2
([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => [8,4,2] => 2
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [6,2,2] => 3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [3,2] => 2
([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7) => [14,2] => 2
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) => [10,2] => 1
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [4,3,3] => 2
([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7) => [6,6,6,6,3,3] => 6
([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => [8,3,2] => 3
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => [8,3] => 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => [5,3] => 2
([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) => [13,2] => 1
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) => [9,3] => 2
([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7) => [12,12,12,4] => 3
([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => [8,8] => 2
([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => [24,24,24] => 3
([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [10,4,4] => 0
([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [13,2] => 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => [5,4] => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [4] => 0
([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => [24] => 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [4,4] => 0
([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => [15] => 1
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [5,4] => 1
([(0,4),(0,5),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => [14] => 1
([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7) => [4,4,3] => 1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => [8] => 1
([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => [15] => 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(5,6),(6,4)],7) => [10,10] => 0
([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [5,5] => 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7) => [6,6,6,6,3,3] => 6
([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) => [7,7] => 0
([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7) => [5,5] => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => [6] => 1
([(0,5),(1,3),(1,4),(3,6),(4,6),(6,2),(6,5)],7) => [22] => 0
([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => [18,18,9] => 3
([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => [14] => 1
([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [10,10,10,10] => 0
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [4,4] => 0
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => [6] => 1
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [5,4] => 1
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7) => [12] => 1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [4,2] => 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [6,6] => 2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7) => [10,10,10,10] => 0
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,2),(5,3),(6,3)],7) => [10,10,10,10] => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,6,6,6] => 4
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7) => [10,10,10,10] => 0
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7) => [10,10] => 0
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7) => [8,8] => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [4,4,4,4,4,4] => 0
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) => [14] => 1
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(6,3),(6,4)],7) => [48] => 1
([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) => [10,6] => 1
([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => [11,7,3] => 2
([(0,4),(0,5),(1,3),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [12,4] => 1
([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(6,4),(6,5)],7) => [9,9,9,9,3,3] => 6
([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7) => [10,7] => 0
([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) => [6,4,3] => 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => [11,11,11,11,11,11] => 6
([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => [4,4,4,4,4,4] => 0
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7) => [3,3,3,3,3,3] => 6
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => [3,3,3] => 3
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => [6] => 1
([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => [24] => 1
([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [8,8] => 2
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) => [9,3] => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => [7] => 0
([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => [48] => 1
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => [8,3] => 2
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [12,12,12,12,12,12,4,4] => 6
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => 2
([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7) => [10,10] => 0
([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7) => [24] => 1
([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => [6,3,3,3] => 4
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7) => [12] => 1
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => [6,6,3] => 3
([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => [6,5,3] => 3
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => [5,4] => 1
([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) => [6,5,3] => 3
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) => [6,4,3] => 2
([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7) => [15,15] => 2
([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => [8,3] => 2
([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => [7,4,4] => 0
([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => [10,10,10,10] => 0
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => [7] => 0
([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => [6,5,3] => 3
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => [5,4] => 1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [3,2] => 2
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) => [12] => 1
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,4] => 0
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => [6] => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => 2
([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7) => [3,3,3,3,3,3] => 6
([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) => [7,7] => 0
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => 2
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => [7] => 0
([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => [11,3,3] => 3
([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => [14] => 1
([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => [5,5,5,5,5,5,5,5,5,5,5,5] => 12
([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [5,5] => 2
([(0,6),(1,5),(3,6),(5,2),(5,3),(6,4)],7) => [5,5,4,4] => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [3,3] => 2
([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) => [5,5] => 2
([(1,5),(4,6),(5,4),(6,2),(6,3)],7) => [7,7] => 0
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [3,3] => 2
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [4,4,2,2] => 2
([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,4,2,2] => 2
([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7) => [5,5,5,5] => 4
([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => [5,5] => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => 1
([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 2
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [4,4] => 0
([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => [15,5,5] => 3
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => [7] => 0
([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => [6,3,3,3] => 4
([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => [8,4,2] => 2
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [6,2,2] => 3
([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) => [14,2] => 2
([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) => [10,2] => 1
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7) => [14] => 1
([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) => [11,5] => 2
([(0,6),(1,4),(1,6),(5,2),(5,3),(6,5)],7) => [22] => 0
([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7) => [14,2] => 2
([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) => [13,2] => 1
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [3,2] => 2
([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) => [6,5,3] => 3
([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [5,4] => 1
([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) => [11] => 1
([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7) => [15,5,5] => 3
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [12,4] => 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => [22] => 0
([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7) => [10,4,4] => 0
([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7) => [10,4,4] => 0
([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => [24,12] => 2
([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => [18] => 1
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => [6,6,6,2] => 4
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => [5,4] => 1
([(0,6),(1,3),(1,4),(4,6),(5,2),(6,5)],7) => [17] => 1
([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7) => [4,4,3] => 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [5] => 1
([(0,4),(1,3),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => [18,18,9] => 3
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => [15] => 1
([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) => [24] => 1
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => [5,5] => 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => 1
([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7) => [18] => 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [4,4,3] => 1
([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) => [8] => 1
([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => [48] => 1
([(0,5),(1,3),(1,4),(2,6),(3,6),(4,6),(5,2)],7) => [12,12,12,4] => 3
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [8] => 1
([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [12,12,12,12,12,12,12,12,12,12] => 10
([(0,3),(0,4),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => [14] => 1
([(0,6),(1,2),(1,4),(2,6),(3,5),(4,5),(6,3)],7) => [14] => 1
([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(5,4),(6,4)],7) => [22] => 0
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7) => [6,6] => 2
([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7) => [14] => 1
([(0,5),(0,6),(1,3),(1,5),(1,6),(3,4),(4,2),(6,4)],7) => [24] => 1
([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => [8,3,2] => 3
([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) => [13,2] => 1
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => [5,3] => 2
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => [9,5] => 2
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => [5,3] => 2
([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => [8,3] => 2
([(0,5),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4)],7) => [12,4] => 1
([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7) => [10,5] => 1
([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) => [12] => 1
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => [6] => 1
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => [3,3,3] => 3
([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => [10,10] => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => [6] => 1
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) => [10] => 0
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => 2
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [3,2] => 2
([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => [9,5] => 2
([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => [5,4] => 1
([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7) => [10,7] => 0
([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => [9,3] => 2
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => 1
([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7) => [10,10] => 0
([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => [8] => 1
([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7) => [12] => 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => [5,5] => 2
([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7) => [18] => 1
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => [6] => 1
([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) => [13] => 0
([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => [4,4,4] => 0
([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7) => [10,10,10] => 0
([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 0
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => 1
([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => [14,2] => 2
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [4] => 0
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => [5] => 1
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => [7] => 0
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => [3,3,3] => 3
([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => [5,5,5,5,5,5] => 6
([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7) => [5,5,5,5,5,5] => 6
([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) => [13] => 0
([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [4,3,3] => 2
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [4,2] => 1
([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7) => [10,5] => 1
([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [5,4] => 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => 1
([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) => [11] => 1
([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => [5,5] => 2
([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) => [9,3] => 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => 0
([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [15] => 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 1
([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [15] => 1
([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => [18,18,9] => 3
([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6] => 10
([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) => [18] => 1
([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => [6,6,6,6,3,3] => 6
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [4,4,4] => 0
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [6,6,3] => 3
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [4,2] => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 16
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => [24,12] => 2
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4)],7) => [10,10] => 0
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => [8] => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => 1
([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7) => [12] => 1
([(0,6),(1,4),(2,6),(3,5),(4,2),(4,3),(6,5)],7) => [14] => 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 0
([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => [24] => 1
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => 1
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [6,6,6,2] => 4
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [4] => 0
([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9) => [9,9,9,9,3,3] => 6
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => [12,4] => 1
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [6,6,6,2] => 4
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [3,2] => 2
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => [8,4,2] => 2
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => [10,2] => 1
([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [10,2] => 1
([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12) => [24,24,24,24,14] => 5
([(0,7),(1,13),(2,12),(3,9),(4,11),(5,6),(5,12),(6,4),(6,8),(7,2),(7,5),(8,11),(8,13),(10,9),(11,10),(12,1),(12,8),(13,3),(13,10)],14) => [15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 22
([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 22
([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => [9,9,9,9,3,3] => 6
([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [58,38,38,38,30] => 4
([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => [98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 12
([(0,6),(0,7),(1,9),(2,8),(3,5),(4,2),(5,1),(5,8),(6,3),(7,4),(8,9)],10) => [26,13,7,7,2] => 2
([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11) => [10,10,10,5,5,2] => 3
([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3] => 41
([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10) => [10,2] => 1
([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11) => [10,2] => 1
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11) => [12,12,4,3,2] => 4
([(0,7),(1,10),(2,11),(3,8),(4,9),(5,2),(5,9),(6,3),(6,12),(7,4),(7,5),(8,10),(9,6),(9,11),(11,12),(12,1),(12,8)],13) => [16,16,16,16,8,4,2] => 2
([(0,8),(2,13),(3,11),(4,9),(5,10),(6,3),(6,10),(7,4),(7,12),(8,5),(8,6),(9,13),(10,7),(10,11),(11,12),(12,2),(12,9),(13,1)],14) => [16,16,16,16,8,4,2] => 2
([(0,5),(1,6),(2,9),(3,6),(3,9),(4,7),(5,1),(5,2),(5,3),(6,8),(8,7),(9,4),(9,8)],10) => [9,9,9,9,3,3] => 6
([(0,6),(1,12),(2,11),(3,11),(3,12),(4,8),(5,9),(6,1),(6,2),(6,3),(7,8),(7,9),(8,10),(9,10),(11,4),(11,7),(12,5),(12,7)],13) => [74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 18
([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [26,13,7,7,2] => 2
([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11) => [10,2] => 1
([(0,7),(0,8),(1,9),(2,10),(3,6),(3,9),(4,3),(5,1),(6,2),(6,11),(7,4),(8,5),(9,11),(11,10)],12) => [42,34,30,22,22,14,2] => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 4,8,4 15,25,17,1,2,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 4 + 8\ q + 4\ q^{2}$
$F_{5} = 15 + 25\ q + 17\ q^{2} + q^{3} + 2\ q^{4} + q^{6} + q^{12} + q^{24}$
Description
The number of parts of a partition that are not congruent 1 modulo 3.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
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