Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001869: Graphs ⟶ ℤ
Values
[1] => [1] => [1] => ([],1) => 0
[1,2] => [1,2] => [2] => ([],2) => 0
[2,1] => [1,2] => [2] => ([],2) => 0
[1,2,3] => [1,2,3] => [3] => ([],3) => 0
[1,3,2] => [1,2,3] => [3] => ([],3) => 0
[2,1,3] => [1,2,3] => [3] => ([],3) => 0
[2,3,1] => [1,2,3] => [3] => ([],3) => 0
[3,1,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[3,2,1] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,2,3,4] => [1,2,3,4] => [4] => ([],4) => 0
[1,2,4,3] => [1,2,3,4] => [4] => ([],4) => 0
[1,3,2,4] => [1,2,3,4] => [4] => ([],4) => 0
[1,3,4,2] => [1,2,3,4] => [4] => ([],4) => 0
[1,4,2,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,4,3,2] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[2,1,3,4] => [1,2,3,4] => [4] => ([],4) => 0
[2,1,4,3] => [1,2,3,4] => [4] => ([],4) => 0
[2,3,1,4] => [1,2,3,4] => [4] => ([],4) => 0
[2,3,4,1] => [1,2,3,4] => [4] => ([],4) => 0
[2,4,1,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[2,4,3,1] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[3,1,2,4] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,1,4,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[3,2,1,4] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,2,4,1] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[3,4,1,2] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,4,2,1] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,1,2,3] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[4,1,3,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,2,1,3] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[4,2,3,1] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,3,1,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,3,2,1] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,2,3,4,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,2,3,5,4] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,2,4,3,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,2,4,5,3] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,2,5,3,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,2,5,4,3] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,3,2,4,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,3,2,5,4] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,3,4,2,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,3,4,5,2] => [1,2,3,4,5] => [5] => ([],5) => 0
[1,3,5,2,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,3,5,4,2] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,4,2,3,5] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,2,5,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,4,3,2,5] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,3,5,2] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,4,5,2,3] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,5,3,2] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,2,3,4] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[1,5,2,4,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,3,2,4] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[1,5,3,4,2] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,4,2,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,4,3,2] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,1,3,4,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,1,3,5,4] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,1,4,3,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,1,4,5,3] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,1,5,3,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,1,5,4,3] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,3,1,4,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,3,1,5,4] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,3,4,1,5] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,3,4,5,1] => [1,2,3,4,5] => [5] => ([],5) => 0
[2,3,5,1,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,3,5,4,1] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,4,1,3,5] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,1,5,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,4,3,1,5] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,3,5,1] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,4,5,1,3] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,5,3,1] => [1,2,4,3,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,1,3,4] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[2,5,1,4,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,3,1,4] => [1,2,5,4,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[2,5,3,4,1] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,4,1,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,4,3,1] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,1,2,4,5] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,1,2,5,4] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,1,4,2,5] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,1,4,5,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,1,5,2,4] => [1,3,5,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[3,1,5,4,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,2,1,4,5] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,2,1,5,4] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,2,4,1,5] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,2,4,5,1] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[3,2,5,1,4] => [1,3,5,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[3,2,5,4,1] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,4,1,2,5] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,1,5,2] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,2,1,5] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,2,5,1] => [1,3,2,4,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,5,1,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,4,5,2,1] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,5,1,2,4] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,5,1,4,2] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,5,2,4,1] => [1,3,2,5,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[3,5,4,1,2] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,5,4,2,1] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,1,2,3,5] => [1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,1,2,5,3] => [1,4,5,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[4,1,3,2,5] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,1,3,5,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,1,5,2,3] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,1,5,3,2] => [1,4,3,5,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,2,1,3,5] => [1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,2,1,5,3] => [1,4,5,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[4,2,3,1,5] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,2,3,5,1] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,2,5,1,3] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,2,5,3,1] => [1,4,3,5,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,3,1,2,5] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,1,5,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,3,2,1,5] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,2,5,1] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,3,5,1,2] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,5,2,1] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,5,1,2,3] => [1,4,2,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,5,1,3,2] => [1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,5,2,1,3] => [1,4,2,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,5,2,3,1] => [1,4,3,2,5] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,5,3,1,2] => [1,4,2,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[4,5,3,2,1] => [1,4,2,5,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,1,2,3,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[5,1,2,4,3] => [1,5,3,2,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,1,3,2,4] => [1,5,4,2,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,1,3,4,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,1,4,2,3] => [1,5,3,4,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,1,4,3,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,2,1,3,4] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[5,2,1,4,3] => [1,5,3,2,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,2,3,1,4] => [1,5,4,2,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,2,3,4,1] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,2,4,1,3] => [1,5,3,4,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,2,4,3,1] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,3,1,2,4] => [1,5,4,2,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,1,4,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,3,2,1,4] => [1,5,4,2,3] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,2,4,1] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,3,4,1,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,3,4,2,1] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,4,1,2,3] => [1,5,3,2,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,4,1,3,2] => [1,5,2,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,4,2,1,3] => [1,5,3,2,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,4,2,3,1] => [1,5,2,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,4,3,1,2] => [1,5,2,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[5,4,3,2,1] => [1,5,2,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,3,6,4,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,3,6,5,4] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,4,3,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,2,4,6,3,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,4,6,5,3] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,5,3,4,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,3,6,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,5,4,3,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,4,6,3] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,2,5,6,3,4] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,6,4,3] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,2,6,3,5,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,2,6,4,5,3] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,3,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,4,3] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,2,4,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,2,6,4,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,2,6,5,4] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,4,2,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[1,3,4,6,2,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,4,6,5,2] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,5,2,4,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,2,6,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,5,4,2,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,4,6,2] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,3,5,6,2,4] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,6,4,2] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,2,4,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,3,6,2,5,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,4,2,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,3,6,4,5,2] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,2,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,4,2] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,2,3,5,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,2,3,6,5] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,2,5,3,6] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,2,5,6,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,4,2,6,3,5] => [1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,4,2,6,5,3] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,3,2,5,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,3,2,6,5] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,3,5,2,6] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,3,5,6,2] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,4,3,6,2,5] => [1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,4,3,6,5,2] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,2,3,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,5,2,6,3] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,5,3,2,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,5,3,6,2] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,4,5,6,2,3] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,6,3,2] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,2,3,5] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,4,6,2,5,3] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,4,6,3,2,5] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,4,6,3,5,2] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,4,6,5,2,3] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,5,3,2] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,2,3,4,6] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,2,3,6,4] => [1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,5,2,4,3,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,2,4,6,3] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,2,6,3,4] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,2,6,4,3] => [1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,5,3,2,4,6] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,3,2,6,4] => [1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[1,5,3,4,2,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,3,4,6,2] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,3,6,2,4] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,3,6,4,2] => [1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,5,4,2,3,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,4,2,6,3] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,3,2,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,4,3,6,2] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,6,2,3] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,4,6,3,2] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,5,6,2,3,4] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,5,6,2,4,3] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,6,3,2,4] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,5,6,3,4,2] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,6,4,2,3] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,5,6,4,3,2] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,2,3,4,5] => [1,2,6,5,4,3] => [3,1,1,1] => ([(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) => 9
[1,6,2,3,5,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,2,4,3,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,2,4,5,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,2,5,3,4] => [1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,2,5,4,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,3,2,4,5] => [1,2,6,5,4,3] => [3,1,1,1] => ([(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) => 9
[1,6,3,2,5,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,3,4,2,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,3,4,5,2] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,3,5,2,4] => [1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,3,5,4,2] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,4,2,3,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,4,2,5,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,4,3,2,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,4,3,5,2] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,4,5,2,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,4,5,3,2] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,6,5,2,3,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,5,2,4,3] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,5,3,2,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,5,3,4,2] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,5,4,2,3] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[1,6,5,4,3,2] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,1,3,4,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,3,5,6,4] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,3,6,4,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,3,6,5,4] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,4,3,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,4,3,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,4,5,3,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,4,5,6,3] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,1,4,6,3,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,4,6,5,3] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,5,3,4,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,3,6,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,5,4,3,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,4,6,3] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,1,5,6,3,4] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,6,4,3] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,3,4,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,1,6,3,5,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,4,3,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,1,6,4,5,3] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,5,3,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,5,4,3] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,1,4,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,1,4,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,1,5,4,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,1,5,6,4] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,1,6,4,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,1,6,5,4] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,4,1,5,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,4,1,6,5] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,4,5,1,6] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [6] => ([],6) => 0
[2,3,4,6,1,5] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,4,6,5,1] => [1,2,3,4,6,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,5,1,4,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,1,6,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,5,4,1,6] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,4,6,1] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,3,5,6,1,4] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,4,1] => [1,2,3,5,4,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,1,4,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,3,6,1,5,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,1,5] => [1,2,3,6,5,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,1,4] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,3,5,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,1,3,6,5] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,1,5,3,6] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,5,6,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,1,6,3,5] => [1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,4,1,6,5,3] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,1,5,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,3,1,6,5] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,3,5,1,6] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,5,6,1] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[2,4,3,6,1,5] => [1,2,4,6,5,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,4,3,6,5,1] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,1,3,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,5,1,6,3] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,5,3,1,6] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,5,3,6,1] => [1,2,4,3,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,4,5,6,1,3] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,6,3,1] => [1,2,4,6,3,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,1,3,5] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,4,6,1,5,3] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,4,6,3,1,5] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,4,6,3,5,1] => [1,2,4,3,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,4,6,5,1,3] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,5,3,1] => [1,2,4,5,3,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,3,4,6] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,1,3,6,4] => [1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,5,1,4,3,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,1,4,6,3] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,6,3,4] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,1,6,4,3] => [1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,5,3,1,4,6] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,3,1,6,4] => [1,2,5,6,4,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[2,5,3,4,1,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,3,4,6,1] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,6,1,4] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,3,6,4,1] => [1,2,5,4,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,5,4,1,3,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,4,1,6,3] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,3,1,6] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,4,3,6,1] => [1,2,5,6,3,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,6,1,3] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,4,6,3,1] => [1,2,5,3,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,5,6,1,3,4] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,5,6,1,4,3] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,6,3,1,4] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,5,6,3,4,1] => [1,2,5,4,3,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,6,4,1,3] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,5,6,4,3,1] => [1,2,5,3,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,1,3,4,5] => [1,2,6,5,4,3] => [3,1,1,1] => ([(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) => 9
[2,6,1,3,5,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,1,4,3,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,1,4,5,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,1,5,3,4] => [1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,1,5,4,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,3,1,4,5] => [1,2,6,5,4,3] => [3,1,1,1] => ([(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) => 9
[2,6,3,1,5,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,3,4,1,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,3,4,5,1] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,3,5,1,4] => [1,2,6,4,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,3,5,4,1] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,4,1,3,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,4,1,5,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,4,3,1,5] => [1,2,6,5,3,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,4,3,5,1] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,4,5,1,3] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,4,5,3,1] => [1,2,6,3,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[2,6,5,1,3,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,5,1,4,3] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,5,3,1,4] => [1,2,6,4,3,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,5,3,4,1] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,5,4,1,3] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[2,6,5,4,3,1] => [1,2,6,3,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,1,2,4,5,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,2,4,6,5] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,2,5,4,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,2,5,6,4] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,2,6,4,5] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,1,2,6,5,4] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,1,4,2,5,6] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,1,4,2,6,5] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,1,4,5,2,6] => [1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,4,5,6,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,1,4,6,2,5] => [1,3,4,6,5,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,1,4,6,5,2] => [1,3,4,6,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,2,4,6] => [1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,1,5,2,6,4] => [1,3,5,6,4,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,1,5,4,2,6] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,1,5,4,6,2] => [1,3,5,6,2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,6,2,4] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,1,5,6,4,2] => [1,3,5,4,6,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,1,6,2,4,5] => [1,3,6,5,4,2] => [3,1,1,1] => ([(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) => 9
[3,1,6,2,5,4] => [1,3,6,4,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,1,6,4,2,5] => [1,3,6,5,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,1,6,4,5,2] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,1,6,5,2,4] => [1,3,6,4,5,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,1,6,5,4,2] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,1,4,5,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,2,1,4,6,5] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,2,1,5,4,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,2,1,5,6,4] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,2,1,6,4,5] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,1,6,5,4] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,4,1,5,6] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,4,1,6,5] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,4,5,1,6] => [1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,4,5,6,1] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[3,2,4,6,1,5] => [1,3,4,6,5,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,2,4,6,5,1] => [1,3,4,6,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,1,4,6] => [1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,5,1,6,4] => [1,3,5,6,4,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,2,5,4,1,6] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,5,4,6,1] => [1,3,5,6,2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,6,1,4] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,5,6,4,1] => [1,3,5,4,6,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,2,6,1,4,5] => [1,3,6,5,4,2] => [3,1,1,1] => ([(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) => 9
[3,2,6,1,5,4] => [1,3,6,4,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,6,4,1,5] => [1,3,6,5,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,2,6,4,5,1] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,2,6,5,1,4] => [1,3,6,4,5,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,2,6,5,4,1] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,1,2,5,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,2,6,5] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,5,2,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,5,6,2] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,6,2,5] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,1,6,5,2] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,2,1,5,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,2,1,6,5] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,2,5,1,6] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,2,5,6,1] => [1,3,2,4,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,2,6,1,5] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,2,6,5,1] => [1,3,2,4,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,5,1,2,6] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,5,1,6,2] => [1,3,5,6,2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,2,1,6] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,5,2,6,1] => [1,3,5,6,2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,6,1,2] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,5,6,2,1] => [1,3,5,2,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,6,1,2,5] => [1,3,6,5,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,6,1,5,2] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,6,2,1,5] => [1,3,6,5,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,4,6,2,5,1] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,6,5,1,2] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,4,6,5,2,1] => [1,3,6,2,4,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,5,1,2,4,6] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,1,2,6,4] => [1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,1,4,2,6] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,1,4,6,2] => [1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,1,6,2,4] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,1,6,4,2] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,2,1,4,6] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,2,1,6,4] => [1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,2,4,1,6] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,2,4,6,1] => [1,3,2,5,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,2,6,1,4] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,2,6,4,1] => [1,3,2,5,4,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,5,4,1,2,6] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,5,4,1,6,2] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,5,4,2,1,6] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,5,4,2,6,1] => [1,3,4,2,5,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[3,5,4,6,1,2] => [1,3,4,6,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,6,2,1] => [1,3,4,6,2,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,1,2,4] => [1,3,6,4,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,6,1,4,2] => [1,3,6,2,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,5,6,2,1,4] => [1,3,6,4,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,5,6,2,4,1] => [1,3,6,2,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,5,6,4,1,2] => [1,3,6,2,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,5,6,4,2,1] => [1,3,6,2,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,1,2,4,5] => [1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,6,1,2,5,4] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,1,4,2,5] => [1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,6,1,4,5,2] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,1,5,2,4] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,1,5,4,2] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,2,1,4,5] => [1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,6,2,1,5,4] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,2,4,1,5] => [1,3,2,6,5,4] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[3,6,2,4,5,1] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,2,5,1,4] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,2,5,4,1] => [1,3,2,6,4,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[3,6,4,1,2,5] => [1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,4,1,5,2] => [1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,4,2,1,5] => [1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,4,2,5,1] => [1,3,4,2,6,5] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,4,5,1,2] => [1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,5,2,1] => [1,3,4,5,2,6] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,1,2,4] => [1,3,5,2,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,5,1,4,2] => [1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,6,5,2,1,4] => [1,3,5,2,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,5,2,4,1] => [1,3,5,4,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[3,6,5,4,1,2] => [1,3,5,2,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[3,6,5,4,2,1] => [1,3,5,2,6,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,1,2,3,5,6] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,2,3,6,5] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,2,5,3,6] => [1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,2,5,6,3] => [1,4,5,6,3,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,1,2,6,3,5] => [1,4,6,5,3,2] => [3,1,1,1] => ([(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) => 9
[4,1,2,6,5,3] => [1,4,6,3,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,3,2,5,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,3,2,6,5] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,3,5,2,6] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,1,3,5,6,2] => [1,4,5,6,2,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,3,6,2,5] => [1,4,6,5,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,3,6,5,2] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,1,5,2,3,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,5,2,6,3] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,5,3,2,6] => [1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,1,5,3,6,2] => [1,4,3,5,6,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,5,6,2,3] => [1,4,6,3,5,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,1,5,6,3,2] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,1,6,2,3,5] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,6,2,5,3] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,1,6,3,2,5] => [1,4,3,6,5,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,1,6,3,5,2] => [1,4,3,6,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,1,6,5,2,3] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,1,6,5,3,2] => [1,4,5,3,6,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,2,1,3,5,6] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,1,3,6,5] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,1,5,3,6] => [1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,1,5,6,3] => [1,4,5,6,3,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,2,1,6,3,5] => [1,4,6,5,3,2] => [3,1,1,1] => ([(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) => 9
[4,2,1,6,5,3] => [1,4,6,3,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,3,1,5,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,2,3,1,6,5] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,2,3,5,1,6] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,2,3,5,6,1] => [1,4,5,6,2,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,3,6,1,5] => [1,4,6,5,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,3,6,5,1] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,2,5,1,3,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,2,5,1,6,3] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,2,5,3,1,6] => [1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,2,5,3,6,1] => [1,4,3,5,6,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,5,6,1,3] => [1,4,6,3,5,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,2,5,6,3,1] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,2,6,1,3,5] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,6,1,5,3] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,2,6,3,1,5] => [1,4,3,6,5,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,2,6,3,5,1] => [1,4,3,6,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,2,6,5,1,3] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,2,6,5,3,1] => [1,4,5,3,6,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,3,1,2,5,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,1,2,6,5] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,1,5,2,6] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,1,5,6,2] => [1,4,5,6,2,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,1,6,2,5] => [1,4,6,5,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,1,6,5,2] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,2,1,5,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,2,1,6,5] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,2,5,1,6] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,2,5,6,1] => [1,4,5,6,2,3] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,6,1,5] => [1,4,6,5,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,2,6,5,1] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,5,1,2,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,1,6,2] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,2,1,6] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,2,6,1] => [1,4,2,3,5,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,6,1,2] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,5,6,2,1] => [1,4,6,2,3,5] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,6,1,2,5] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,6,1,5,2] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,6,2,1,5] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,6,2,5,1] => [1,4,2,3,6,5] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,3,6,5,1,2] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,3,6,5,2,1] => [1,4,5,2,3,6] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[4,5,1,2,3,6] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,1,2,6,3] => [1,4,2,5,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,1,3,2,6] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,1,3,6,2] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,1,6,2,3] => [1,4,6,3,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,1,6,3,2] => [1,4,6,2,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,5,2,1,3,6] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,2,1,6,3] => [1,4,2,5,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,2,3,1,6] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,2,3,6,1] => [1,4,3,2,5,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,2,6,1,3] => [1,4,6,3,2,5] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,2,6,3,1] => [1,4,6,2,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,5,3,1,2,6] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,3,1,6,2] => [1,4,2,5,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,3,2,1,6] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,3,2,6,1] => [1,4,2,5,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,5,3,6,1,2] => [1,4,6,2,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,5,3,6,2,1] => [1,4,6,2,5,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,5,6,1,2,3] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,6,1,3,2] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,6,2,1,3] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,6,2,3,1] => [1,4,2,5,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,6,3,1,2] => [1,4,3,6,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,5,6,3,2,1] => [1,4,3,6,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,1,2,3,5] => [1,4,2,6,5,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,6,1,2,5,3] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,1,3,2,5] => [1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,1,3,5,2] => [1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,1,5,2,3] => [1,4,5,2,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,1,5,3,2] => [1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,6,2,1,3,5] => [1,4,2,6,5,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,6,2,1,5,3] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,2,3,1,5] => [1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,2,3,5,1] => [1,4,3,2,6,5] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,2,5,1,3] => [1,4,5,2,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,2,5,3,1] => [1,4,5,3,2,6] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[4,6,3,1,2,5] => [1,4,2,6,5,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,6,3,1,5,2] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,3,2,1,5] => [1,4,2,6,5,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[4,6,3,2,5,1] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,3,5,1,2] => [1,4,5,2,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,3,5,2,1] => [1,4,5,2,6,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[4,6,5,1,2,3] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,5,1,3,2] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,5,2,1,3] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,5,2,3,1] => [1,4,2,6,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,5,3,1,2] => [1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[4,6,5,3,2,1] => [1,4,3,5,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,1,2,3,4,6] => [1,5,4,3,2,6] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,2,3,6,4] => [1,5,6,4,3,2] => [3,1,1,1] => ([(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) => 9
[5,1,2,4,3,6] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,2,4,6,3] => [1,5,6,3,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,2,6,3,4] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,2,6,4,3] => [1,5,4,6,3,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,1,3,2,4,6] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,3,2,6,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,3,4,2,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,3,4,6,2] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,1,3,6,2,4] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,3,6,4,2] => [1,5,4,6,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,1,4,2,3,6] => [1,5,3,4,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,1,4,2,6,3] => [1,5,6,3,4,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,1,4,3,2,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,4,3,6,2] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,1,4,6,2,3] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,4,6,3,2] => [1,5,3,4,6,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,6,2,3,4] => [1,5,3,6,4,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,1,6,2,4,3] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,6,3,2,4] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,6,3,4,2] => [1,5,4,3,6,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,1,6,4,2,3] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,1,6,4,3,2] => [1,5,3,6,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,2,1,3,4,6] => [1,5,4,3,2,6] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,1,3,6,4] => [1,5,6,4,3,2] => [3,1,1,1] => ([(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) => 9
[5,2,1,4,3,6] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,4,6,3] => [1,5,6,3,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,1,6,3,4] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,6,4,3] => [1,5,4,6,3,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,2,3,1,4,6] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,3,1,6,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,3,4,1,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,2,3,4,6,1] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,2,3,6,1,4] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,2,3,6,4,1] => [1,5,4,6,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,2,4,1,3,6] => [1,5,3,4,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,2,4,1,6,3] => [1,5,6,3,4,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,2,4,3,1,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,2,4,3,6,1] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,2,4,6,1,3] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,2,4,6,3,1] => [1,5,3,4,6,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,6,1,3,4] => [1,5,3,6,4,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,2,6,1,4,3] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,6,3,1,4] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,6,3,4,1] => [1,5,4,3,6,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,2,6,4,1,3] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,2,6,4,3,1] => [1,5,3,6,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,1,2,4,6] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,1,2,6,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,1,4,2,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,1,4,6,2] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,3,1,6,2,4] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,1,6,4,2] => [1,5,4,6,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,2,1,4,6] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,1,6,4] => [1,5,6,4,2,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,2,4,1,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,2,4,6,1] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,3,2,6,1,4] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,2,6,4,1] => [1,5,4,6,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,3,4,1,2,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,4,1,6,2] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,3,4,2,1,6] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,4,2,6,1] => [1,5,6,2,3,4] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[5,3,4,6,1,2] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,4,6,2,1] => [1,5,2,3,4,6] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,3,6,1,2,4] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,6,1,4,2] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,6,2,1,4] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,6,2,4,1] => [1,5,4,2,3,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,6,4,1,2] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,3,6,4,2,1] => [1,5,2,3,6,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,1,2,3,6] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,1,2,6,3] => [1,5,6,3,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,1,3,2,6] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,1,3,6,2] => [1,5,6,2,4,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,4,1,6,2,3] => [1,5,2,4,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,1,6,3,2] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,2,1,3,6] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,2,1,6,3] => [1,5,6,3,2,4] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,2,3,1,6] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,2,3,6,1] => [1,5,6,2,4,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,4,2,6,1,3] => [1,5,2,4,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,2,6,3,1] => [1,5,3,2,4,6] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,1,2,6] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,3,1,6,2] => [1,5,6,2,4,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,4,3,2,1,6] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,3,2,6,1] => [1,5,6,2,4,3] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,4,3,6,1,2] => [1,5,2,4,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,3,6,2,1] => [1,5,2,4,6,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,4,6,1,2,3] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,6,1,3,2] => [1,5,3,6,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,6,2,1,3] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,6,2,3,1] => [1,5,3,6,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,6,3,1,2] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,4,6,3,2,1] => [1,5,2,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,1,2,3,4] => [1,5,3,2,6,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,1,2,4,3] => [1,5,4,2,6,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,1,3,2,4] => [1,5,2,6,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,6,1,3,4,2] => [1,5,4,3,2,6] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,6,1,4,2,3] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,1,4,3,2] => [1,5,3,2,6,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,2,1,3,4] => [1,5,3,2,6,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,2,1,4,3] => [1,5,4,2,6,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,2,3,1,4] => [1,5,2,6,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,6,2,3,4,1] => [1,5,4,3,2,6] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[5,6,2,4,1,3] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,2,4,3,1] => [1,5,3,2,6,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,3,1,2,4] => [1,5,2,6,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,6,3,1,4,2] => [1,5,4,2,6,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,3,2,1,4] => [1,5,2,6,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[5,6,3,2,4,1] => [1,5,4,2,6,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[5,6,3,4,1,2] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,3,4,2,1] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,1,2,3] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,1,3,2] => [1,5,3,4,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,2,1,3] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,2,3,1] => [1,5,3,4,2,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,3,1,2] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[5,6,4,3,2,1] => [1,5,2,6,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,1,2,3,4,5] => [1,6,5,4,3,2] => [2,1,1,1,1] => ([(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) => 9
[6,1,2,3,5,4] => [1,6,4,3,2,5] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,1,2,4,3,5] => [1,6,5,3,2,4] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,1,2,4,5,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,2,5,3,4] => [1,6,4,5,3,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,1,2,5,4,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,3,2,4,5] => [1,6,5,4,2,3] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,1,3,2,5,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,3,4,2,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,3,4,5,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,1,3,5,2,4] => [1,6,4,5,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,1,3,5,4,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,1,4,2,3,5] => [1,6,5,3,4,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,1,4,2,5,3] => [1,6,3,4,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,1,4,3,2,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,4,3,5,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,1,4,5,2,3] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,1,4,5,3,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,1,5,2,3,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,5,2,4,3] => [1,6,3,5,4,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,1,5,3,2,4] => [1,6,4,3,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,1,5,3,4,2] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,1,5,4,2,3] => [1,6,3,5,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,1,5,4,3,2] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,1,3,4,5] => [1,6,5,4,3,2] => [2,1,1,1,1] => ([(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) => 9
[6,2,1,3,5,4] => [1,6,4,3,2,5] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,1,4,3,5] => [1,6,5,3,2,4] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,1,4,5,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,1,5,3,4] => [1,6,4,5,3,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,2,1,5,4,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,3,1,4,5] => [1,6,5,4,2,3] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,3,1,5,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,3,4,1,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,3,4,5,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,2,3,5,1,4] => [1,6,4,5,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,2,3,5,4,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,2,4,1,3,5] => [1,6,5,3,4,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,2,4,1,5,3] => [1,6,3,4,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,2,4,3,1,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,4,3,5,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,2,4,5,1,3] => [1,6,3,4,5,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,4,5,3,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,2,5,1,3,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,5,1,4,3] => [1,6,3,5,4,2] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,2,5,3,1,4] => [1,6,4,3,5,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,2,5,3,4,1] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,2,5,4,1,3] => [1,6,3,5,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,2,5,4,3,1] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,1,2,4,5] => [1,6,5,4,2,3] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,1,2,5,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,4,2,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,4,5,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,1,5,2,4] => [1,6,4,5,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,3,1,5,4,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,2,1,4,5] => [1,6,5,4,2,3] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,2,1,5,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,4,1,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,4,5,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,2,5,1,4] => [1,6,4,5,2,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,3,2,5,4,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,4,1,2,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,1,5,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,4,2,1,5] => [1,6,5,2,3,4] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,2,5,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,4,5,1,2] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,4,5,2,1] => [1,6,2,3,4,5] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,3,5,1,2,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,5,1,4,2] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,5,2,1,4] => [1,6,4,2,3,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,5,2,4,1] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,5,4,1,2] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,3,5,4,2,1] => [1,6,2,3,5,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,1,2,3,5] => [1,6,5,3,2,4] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,1,2,5,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,1,3,2,5] => [1,6,5,2,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,4,1,3,5,2] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,1,5,2,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,1,5,3,2] => [1,6,2,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,2,1,3,5] => [1,6,5,3,2,4] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,2,1,5,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,2,3,1,5] => [1,6,5,2,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,4,2,3,5,1] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,2,5,1,3] => [1,6,3,2,4,5] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,2,5,3,1] => [1,6,2,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,3,1,2,5] => [1,6,5,2,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,4,3,1,5,2] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,3,2,1,5] => [1,6,5,2,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,4,3,2,5,1] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,3,5,1,2] => [1,6,2,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,3,5,2,1] => [1,6,2,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,4,5,1,2,3] => [1,6,3,5,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,5,1,3,2] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,5,2,1,3] => [1,6,3,5,2,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,5,2,3,1] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,5,3,1,2] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,4,5,3,2,1] => [1,6,2,4,3,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,1,2,3,4] => [1,6,4,2,5,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,1,2,4,3] => [1,6,3,2,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,1,3,2,4] => [1,6,4,3,2,5] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,5,1,3,4,2] => [1,6,2,5,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,5,1,4,2,3] => [1,6,3,2,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,1,4,3,2] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,2,1,3,4] => [1,6,4,2,5,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,2,1,4,3] => [1,6,3,2,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,2,3,1,4] => [1,6,4,3,2,5] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[6,5,2,3,4,1] => [1,6,2,5,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,5,2,4,1,3] => [1,6,3,2,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,2,4,3,1] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,3,1,2,4] => [1,6,4,2,5,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,3,1,4,2] => [1,6,2,5,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,5,3,2,1,4] => [1,6,4,2,5,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[6,5,3,2,4,1] => [1,6,2,5,4,3] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[6,5,3,4,1,2] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,3,4,2,1] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,1,2,3] => [1,6,3,4,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,1,3,2] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,2,1,3] => [1,6,3,4,2,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,2,3,1] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,3,1,2] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[6,5,4,3,2,1] => [1,6,2,5,3,4] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
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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:
4,0,2 8,0,8,6,2 16,0,24,28,26,16,10 32,0,64,96,120,126,126,96,48,12
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + 2\ q^{2}$
$F_{4} = 8 + 8\ q^{2} + 6\ q^{3} + 2\ q^{4}$
$F_{5} = 16 + 24\ q^{2} + 28\ q^{3} + 26\ q^{4} + 16\ q^{5} + 10\ q^{6}$
$F_{6} = 32 + 64\ q^{2} + 96\ q^{3} + 120\ q^{4} + 126\ q^{5} + 126\ q^{6} + 96\ q^{7} + 48\ q^{8} + 12\ q^{9}$
Description
The maximum cut size of a graph.
A cut is a set of edges which connect different sides of a vertex partition $V = A \sqcup B$.
A cut is a set of edges which connect different sides of a vertex partition $V = A \sqcup B$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
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