Identifier
-
Mp00248:
Permutations
—DEX composition⟶
Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001812: Graphs ⟶ ℤ
Values
[1] => [1] => [1] => ([],1) => 0
[1,2] => [2] => [2] => ([],2) => 0
[2,1] => [2] => [2] => ([],2) => 0
[1,2,3] => [3] => [3] => ([],3) => 0
[1,3,2] => [1,2] => [2,1] => ([(0,2),(1,2)],3) => 1
[2,1,3] => [3] => [3] => ([],3) => 0
[2,3,1] => [3] => [3] => ([],3) => 0
[3,1,2] => [3] => [3] => ([],3) => 0
[3,2,1] => [2,1] => [1,2] => ([(1,2)],3) => 1
[1,2,3,4] => [4] => [4] => ([],4) => 0
[1,2,4,3] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[1,3,2,4] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 1
[1,3,4,2] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 1
[1,4,2,3] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 1
[1,4,3,2] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[2,1,3,4] => [4] => [4] => ([],4) => 0
[2,1,4,3] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[2,3,1,4] => [4] => [4] => ([],4) => 0
[2,3,4,1] => [4] => [4] => ([],4) => 0
[2,4,1,3] => [4] => [4] => ([],4) => 0
[2,4,3,1] => [3,1] => [1,3] => ([(2,3)],4) => 1
[3,1,2,4] => [4] => [4] => ([],4) => 0
[3,1,4,2] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[3,2,1,4] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[3,2,4,1] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[3,4,1,2] => [4] => [4] => ([],4) => 0
[3,4,2,1] => [3,1] => [1,3] => ([(2,3)],4) => 1
[4,1,2,3] => [4] => [4] => ([],4) => 0
[4,1,3,2] => [3,1] => [1,3] => ([(2,3)],4) => 1
[4,2,1,3] => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1
[4,2,3,1] => [3,1] => [1,3] => ([(2,3)],4) => 1
[4,3,1,2] => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 1
[4,3,2,1] => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,2,3,4,5] => [5] => [5] => ([],5) => 0
[1,2,3,5,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[1,2,4,3,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[1,2,4,5,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[1,2,5,3,4] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[1,2,5,4,3] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,2,4,5] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,3,2,5,4] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,4,2,5] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,3,4,5,2] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,3,5,2,4] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,3,5,4,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,2,3,5] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,4,2,5,3] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,3,2,5] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,3,5,2] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,5,2,3] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,4,5,3,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,2,3,4] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[1,5,2,4,3] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,3,2,4] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,3,4,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,4,2,3] => [1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,4,3,2] => [1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[2,1,3,4,5] => [5] => [5] => ([],5) => 0
[2,1,3,5,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,1,4,3,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[2,1,4,5,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[2,1,5,3,4] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[2,1,5,4,3] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,3,1,4,5] => [5] => [5] => ([],5) => 0
[2,3,1,5,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,3,4,1,5] => [5] => [5] => ([],5) => 0
[2,3,4,5,1] => [5] => [5] => ([],5) => 0
[2,3,5,1,4] => [5] => [5] => ([],5) => 0
[2,3,5,4,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[2,4,1,3,5] => [5] => [5] => ([],5) => 0
[2,4,1,5,3] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,4,3,1,5] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,4,3,5,1] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,4,5,1,3] => [5] => [5] => ([],5) => 0
[2,4,5,3,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[2,5,1,3,4] => [5] => [5] => ([],5) => 0
[2,5,1,4,3] => [4,1] => [1,4] => ([(3,4)],5) => 1
[2,5,3,1,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[2,5,3,4,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[2,5,4,1,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[2,5,4,3,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,1,2,4,5] => [5] => [5] => ([],5) => 0
[3,1,2,5,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[3,1,4,2,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,1,4,5,2] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,1,5,2,4] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,1,5,4,2] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,2,1,4,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,2,1,5,4] => [2,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,2,4,1,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,2,4,5,1] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,2,5,1,4] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,2,5,4,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,4,1,2,5] => [5] => [5] => ([],5) => 0
[3,4,1,5,2] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[3,4,2,1,5] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[3,4,2,5,1] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[3,4,5,1,2] => [5] => [5] => ([],5) => 0
[3,4,5,2,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[3,5,1,2,4] => [5] => [5] => ([],5) => 0
[3,5,1,4,2] => [4,1] => [1,4] => ([(3,4)],5) => 1
>>> Load all 833 entries. <<<[3,5,2,1,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[3,5,2,4,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[3,5,4,1,2] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[3,5,4,2,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,1,2,3,5] => [5] => [5] => ([],5) => 0
[4,1,2,5,3] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,1,3,2,5] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,1,3,5,2] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,1,5,2,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[4,1,5,3,2] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,2,1,3,5] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[4,2,1,5,3] => [2,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,2,3,1,5] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,2,3,5,1] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,2,5,1,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[4,2,5,3,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,1,2,5] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[4,3,1,5,2] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,2,1,5] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,2,5,1] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,5,1,2] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[4,3,5,2,1] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,5,1,2,3] => [5] => [5] => ([],5) => 0
[4,5,1,3,2] => [4,1] => [1,4] => ([(3,4)],5) => 1
[4,5,2,1,3] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,5,2,3,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[4,5,3,1,2] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[4,5,3,2,1] => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,1,2,3,4] => [5] => [5] => ([],5) => 0
[5,1,2,4,3] => [4,1] => [1,4] => ([(3,4)],5) => 1
[5,1,3,2,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[5,1,3,4,2] => [4,1] => [1,4] => ([(3,4)],5) => 1
[5,1,4,2,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[5,1,4,3,2] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,2,1,3,4] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[5,2,1,4,3] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,2,3,1,4] => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1
[5,2,3,4,1] => [4,1] => [1,4] => ([(3,4)],5) => 1
[5,2,4,1,3] => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 1
[5,2,4,3,1] => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,3,1,2,4] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[5,3,1,4,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,3,2,1,4] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,3,2,4,1] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,3,4,1,2] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[5,3,4,2,1] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,1,2,3] => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[5,4,1,3,2] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,2,1,3] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,2,3,1] => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,3,1,2] => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[5,4,3,2,1] => [1,2,1,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,2,3,4,5,6] => [6] => [6] => ([],6) => 0
[1,2,3,4,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[1,2,3,5,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[1,2,3,5,6,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[1,2,3,6,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[1,2,3,6,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,3,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,4,3,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,5,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,4,5,6,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,4,6,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,4,6,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,3,4,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,5,3,6,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,4,3,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,4,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,6,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,5,6,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,3,4,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,2,6,3,5,4] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,4,3,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,4,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,5,3,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,5,4,3] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,2,4,5,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,2,4,6,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,5,4,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,5,6,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,6,4,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,4,2,5,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,4,2,6,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,4,5,2,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,4,5,6,2] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,4,6,2,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,4,6,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,2,4,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,5,2,6,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,4,2,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,4,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,6,2,4] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,5,6,4,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,6,2,4,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,3,6,2,5,4] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,6,4,2,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,6,4,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,6,5,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,3,5,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,4,2,3,6,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,5,3,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,5,6,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,6,3,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,2,5,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,2,6,5] => [1,2,1,2] => [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) => 3
[1,4,3,5,2,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,5,6,2] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,6,2,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,2,3,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,4,5,2,6,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,3,2,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,3,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,6,2,3] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,4,5,6,3,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,6,2,3,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,4,6,2,5,3] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,6,3,2,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,6,3,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,6,5,2,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,3,4,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,5,2,3,6,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,4,3,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,4,6,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,6,3,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,2,4,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,2,6,4] => [1,2,1,2] => [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) => 3
[1,5,3,4,2,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,4,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,6,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,2,3,6] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,2,6,3] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,3,2,6] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,3,6,2] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,6,2,3] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,6,3,2] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,2,3,4] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,5,6,2,4,3] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,6,3,2,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,6,3,4,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,6,4,2,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,3,4,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,6,2,3,5,4] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,4,3,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,4,5,3] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,5,3,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,2,4,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,4,2,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,4,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,5,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,4,2,3,5] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,4,2,5,3] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,3,2,5] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,3,5,2] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,5,2,3] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,4,5,3,2] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,2,3,4] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,5,2,4,3] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,3,2,4] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,3,4,2] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,4,2,3] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,1,3,4,5,6] => [6] => [6] => ([],6) => 0
[2,1,3,4,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,1,3,5,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,1,3,5,6,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,1,3,6,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,1,3,6,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,3,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,4,3,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,5,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,4,5,6,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,4,6,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,4,6,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,3,4,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,5,3,6,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,3,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,6,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,5,6,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,3,4,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,1,6,3,5,4] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,3,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,3,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,4,3] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,3,1,4,5,6] => [6] => [6] => ([],6) => 0
[2,3,1,4,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,1,5,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,3,1,5,6,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,3,1,6,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,3,1,6,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,4,1,5,6] => [6] => [6] => ([],6) => 0
[2,3,4,1,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,4,5,1,6] => [6] => [6] => ([],6) => 0
[2,3,4,5,6,1] => [6] => [6] => ([],6) => 0
[2,3,4,6,1,5] => [6] => [6] => ([],6) => 0
[2,3,4,6,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,3,5,1,4,6] => [6] => [6] => ([],6) => 0
[2,3,5,1,6,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,5,4,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,5,4,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,5,6,1,4] => [6] => [6] => ([],6) => 0
[2,3,5,6,4,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,3,6,1,4,5] => [6] => [6] => ([],6) => 0
[2,3,6,1,5,4] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,3,6,4,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,3,6,4,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,3,6,5,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,3,6,5,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,1,3,5,6] => [6] => [6] => ([],6) => 0
[2,4,1,3,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,4,1,5,3,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,1,5,6,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,1,6,3,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,1,6,5,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,3,1,5,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,3,1,6,5] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,3,5,1,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,3,5,6,1] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,3,6,1,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,3,6,5,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,5,1,3,6] => [6] => [6] => ([],6) => 0
[2,4,5,1,6,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,4,5,3,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,4,5,3,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,4,5,6,1,3] => [6] => [6] => ([],6) => 0
[2,4,5,6,3,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,4,6,1,3,5] => [6] => [6] => ([],6) => 0
[2,4,6,1,5,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,4,6,3,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,4,6,3,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,4,6,5,1,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,4,6,5,3,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,1,3,4,6] => [6] => [6] => ([],6) => 0
[2,5,1,3,6,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,1,4,3,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,1,4,6,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,1,6,3,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,5,1,6,4,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,3,1,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,5,3,1,6,4] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,3,4,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,3,4,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,3,6,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,5,3,6,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,4,1,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,5,4,1,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,4,3,1,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,4,3,6,1] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,4,6,1,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,5,4,6,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,6,1,3,4] => [6] => [6] => ([],6) => 0
[2,5,6,1,4,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,5,6,3,1,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,6,3,4,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,5,6,4,1,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,5,6,4,3,1] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[2,6,1,3,4,5] => [6] => [6] => ([],6) => 0
[2,6,1,3,5,4] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,6,1,4,3,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,6,1,4,5,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,6,1,5,3,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,6,1,5,4,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,3,1,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,6,3,1,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,3,4,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[2,6,3,4,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[2,6,3,5,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[2,6,3,5,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,4,1,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,6,4,1,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,4,3,1,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,4,3,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,4,5,1,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,6,4,5,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,5,1,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[2,6,5,1,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,5,3,1,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,5,3,4,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,5,4,1,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,5,4,3,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,1,2,4,5,6] => [6] => [6] => ([],6) => 0
[3,1,2,4,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,1,2,5,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,1,2,5,6,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,1,2,6,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,1,2,6,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,2,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,4,2,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,2,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,4,5,6,2] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,4,6,2,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,4,6,5,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,2,4,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,5,2,6,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,4,2,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,4,6,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,6,2,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,5,6,4,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,2,4,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,1,6,2,5,4] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,4,2,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,4,5,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,5,2,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,5,4,2] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,1,4,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,1,4,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,5,4,6] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,5,6,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,6,4,5] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,6,5,4] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,4,1,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,4,1,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,1,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,4,5,6,1] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,4,6,1,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,4,6,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,1,4,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,5,1,6,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,4,1,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,4,6,1] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,6,1,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,5,6,4,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,1,4,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,2,6,1,5,4] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,4,1,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,4,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,5,1,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,5,4,1] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,1,2,5,6] => [6] => [6] => ([],6) => 0
[3,4,1,2,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,4,1,5,2,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,1,5,6,2] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,1,6,2,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,1,6,5,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,2,1,5,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,2,1,6,5] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,2,5,1,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,2,5,6,1] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,2,6,1,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,2,6,5,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,5,1,2,6] => [6] => [6] => ([],6) => 0
[3,4,5,1,6,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,4,5,2,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,4,5,2,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,4,5,6,1,2] => [6] => [6] => ([],6) => 0
[3,4,5,6,2,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,4,6,1,2,5] => [6] => [6] => ([],6) => 0
[3,4,6,1,5,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,4,6,2,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,4,6,2,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,4,6,5,1,2] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,4,6,5,2,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,1,2,4,6] => [6] => [6] => ([],6) => 0
[3,5,1,2,6,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,1,4,2,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,1,4,6,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,1,6,2,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,5,1,6,4,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,2,1,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,5,2,1,6,4] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,2,4,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,2,4,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,2,6,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,5,2,6,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,4,1,2,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,5,4,1,6,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,4,2,1,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,4,2,6,1] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,4,6,1,2] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,5,4,6,2,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,6,1,2,4] => [6] => [6] => ([],6) => 0
[3,5,6,1,4,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,5,6,2,1,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,6,2,4,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,5,6,4,1,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,5,6,4,2,1] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,1,2,4,5] => [6] => [6] => ([],6) => 0
[3,6,1,2,5,4] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,6,1,4,2,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,6,1,4,5,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,6,1,5,2,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,6,1,5,4,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,2,1,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,6,2,1,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,2,4,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[3,6,2,4,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[3,6,2,5,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[3,6,2,5,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,4,1,2,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,6,4,1,5,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,4,2,1,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,4,2,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,4,5,1,2] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,6,4,5,2,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,5,1,2,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[3,6,5,1,4,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,5,2,1,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,5,2,4,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,5,4,1,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,5,4,2,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,2,3,5,6] => [6] => [6] => ([],6) => 0
[4,1,2,3,6,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,1,2,5,3,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,2,5,6,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,2,6,3,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,2,6,5,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,2,5,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,3,2,6,5] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,2,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,3,5,6,2] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,3,6,2,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,1,3,6,5,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,2,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,1,5,2,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,3,2,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,3,6,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,6,2,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,1,5,6,3,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,2,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,1,6,2,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,3,2,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,3,5,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,5,2,3] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,5,3,2] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,3,5,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,2,1,3,6,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,5,3,6] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,5,6,3] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,6,3,5] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,6,5,3] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,3,1,5,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,2,3,1,6,5] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,1,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,2,3,5,6,1] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,2,3,6,1,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,2,3,6,5,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,1,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,2,5,1,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,3,1,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,3,6,1] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,6,1,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,2,5,6,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,1,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,2,6,1,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,3,1,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,3,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,5,1,3] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,5,3,1] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,2,5,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,3,1,2,6,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,5,2,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,5,6,2] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,6,2,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,1,5,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,1,6,5] => [1,2,1,2] => [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) => 3
[4,3,2,5,1,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,5,6,1] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,6,1,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,1,2,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,3,5,1,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,2,1,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,2,6,1] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,6,1,2] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,3,5,6,2,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,1,2,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,3,6,1,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,2,1,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,2,5,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,5,1,2] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,1,2,3,6] => [6] => [6] => ([],6) => 0
[4,5,1,2,6,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,1,3,2,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,1,3,6,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,1,6,2,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,5,1,6,3,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,2,1,3,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,5,2,1,6,3] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,2,3,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,2,3,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,2,6,1,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,5,2,6,3,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,3,1,2,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,5,3,1,6,2] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,3,2,1,6] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,3,2,6,1] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,3,6,1,2] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,5,3,6,2,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,6,1,2,3] => [6] => [6] => ([],6) => 0
[4,5,6,1,3,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[4,5,6,2,1,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,6,2,3,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[4,5,6,3,1,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,5,6,3,2,1] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,1,2,3,5] => [6] => [6] => ([],6) => 0
[4,6,1,2,5,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[4,6,1,3,2,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,6,1,3,5,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[4,6,1,5,2,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,6,1,5,3,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,2,1,3,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,6,2,1,5,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,2,3,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[4,6,2,3,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[4,6,2,5,1,3] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,6,2,5,3,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,3,1,2,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,6,3,1,5,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,3,2,1,5] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,3,2,5,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,3,5,1,2] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[4,6,3,5,2,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,5,1,2,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[4,6,5,1,3,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,5,2,1,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,5,2,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,5,3,1,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,5,3,2,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,2,3,4,6] => [6] => [6] => ([],6) => 0
[5,1,2,3,6,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,1,2,4,3,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,1,2,4,6,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,1,2,6,3,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,1,2,6,4,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,2,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,1,3,2,6,4] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,4,2,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,1,3,4,6,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,1,3,6,2,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,1,3,6,4,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,2,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,1,4,2,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,3,2,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,3,6,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,6,2,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,1,4,6,3,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,2,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,1,6,2,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,3,2,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,3,4,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,4,2,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,4,3,2] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,3,4,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,2,1,3,6,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,4,3,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,4,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,6,3,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,6,4,3] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,3,1,4,6] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,2,3,1,6,4] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,3,4,1,6] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,2,3,4,6,1] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,2,3,6,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,2,3,6,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,1,3,6] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,2,4,1,6,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,3,1,6] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,3,6,1] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,6,1,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,2,4,6,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,1,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,2,6,1,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,3,1,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,3,4,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,4,1,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,4,3,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,2,4,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,3,1,2,6,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,1,4,2,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,1,4,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,1,6,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,1,4,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,1,6,4] => [1,2,1,2] => [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) => 3
[5,3,2,4,1,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,4,6,1] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,6,1,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,1,2,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,3,4,1,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,2,1,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,2,6,1] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,6,1,2] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,3,4,6,2,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,1,2,4] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,3,6,1,4,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,2,1,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,2,4,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,4,1,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,2,3,6] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,4,1,2,6,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,3,2,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,3,6,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,6,2,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,1,3,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,1,6,3] => [1,2,1,2] => [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) => 3
[5,4,2,3,1,6] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,3,6,1] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,6,1,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,3,1,2,6] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,3,1,6,2] => [1,2,1,2] => [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) => 3
[5,4,3,2,1,6] => [1,2,1,2] => [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) => 3
[5,4,3,2,6,1] => [1,2,1,2] => [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) => 3
[5,4,3,6,1,2] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,1,2,3] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,4,6,1,3,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,2,1,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,2,3,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,3,1,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,1,2,3,4] => [6] => [6] => ([],6) => 0
[5,6,1,2,4,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[5,6,1,3,2,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,6,1,3,4,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[5,6,1,4,2,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,6,1,4,3,2] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,2,1,3,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,6,2,1,4,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,2,3,1,4] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,6,2,3,4,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[5,6,2,4,1,3] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,6,2,4,3,1] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,3,1,2,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[5,6,3,1,4,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,3,2,1,4] => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,3,2,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,3,4,1,2] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[5,6,3,4,2,1] => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,4,1,2,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[5,6,4,1,3,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,4,2,1,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,4,2,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,4,3,1,2] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,4,3,2,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,2,3,4,5] => [6] => [6] => ([],6) => 0
[6,1,2,3,5,4] => [5,1] => [1,5] => ([(4,5)],6) => 1
[6,1,2,4,3,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[6,1,2,4,5,3] => [5,1] => [1,5] => ([(4,5)],6) => 1
[6,1,2,5,3,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[6,1,2,5,4,3] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,2,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[6,1,3,2,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,4,2,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[6,1,3,4,5,2] => [5,1] => [1,5] => ([(4,5)],6) => 1
[6,1,3,5,2,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[6,1,3,5,4,2] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,2,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,1,4,2,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,3,2,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,3,5,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,5,2,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,1,4,5,3,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,2,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,1,5,2,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,3,2,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,3,4,2] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,4,2,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,4,3,2] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,1,3,4,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,2,1,3,5,4] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,4,3,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,4,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,5,3,4] => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,5,4,3] => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,3,1,4,5] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[6,2,3,1,5,4] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,3,4,1,5] => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1
[6,2,3,4,5,1] => [5,1] => [1,5] => ([(4,5)],6) => 1
[6,2,3,5,1,4] => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 1
[6,2,3,5,4,1] => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,1,3,5] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,2,4,1,5,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,3,1,5] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,3,5,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,5,1,3] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,2,4,5,3,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,1,3,4] => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,2,5,1,4,3] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,3,1,4] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,3,4,1] => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,4,1,3] => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,4,3,1] => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,1,2,4,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,3,1,2,5,4] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,1,4,2,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,1,4,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,1,5,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,1,4,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,4,1,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,4,5,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,5,1,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,1,2,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,3,4,1,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,2,1,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,2,5,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,5,1,2] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,3,4,5,2,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,1,2,4] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,3,5,1,4,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,2,1,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,2,4,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,4,1,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,2,3,5] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,4,1,2,5,3] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,3,2,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,3,5,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,5,2,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,1,3,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,3,1,5] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,3,5,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,5,1,3] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,3,1,2,5] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,3,2,1,5] => [1,2,1,2] => [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) => 3
[6,4,3,5,1,2] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,1,2,3] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,4,5,1,3,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,2,1,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,2,3,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,3,1,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,2,3,4] => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[6,5,1,2,4,3] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,3,2,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,3,4,2] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,4,2,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,1,3,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,3,1,4] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,3,4,1] => [1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,4,1,3] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,3,1,2,4] => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,3,2,1,4] => [1,2,1,2] => [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) => 3
[6,5,3,4,1,2] => [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,4,1,2,3] => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,4,1,3,2] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,4,2,1,3] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,4,2,3,1] => [1,1,3,1] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,4,3,1,2] => [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
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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:
4,2 8,14,2 16,66,36,2
F1=1
F2=2
F3=4+2 q
F4=8+14 q+2 q2
F5=16+66 q+36 q2+2 q3
Description
The biclique partition number of a graph.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph Kn has biclique partition number n−1.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph Kn has biclique partition number n−1.
Map
DEX composition
Description
The DEX composition of a permutation.
Let π be a permutation in Sn. Let ˉπ be the word in the ordered set ˉ1<⋯<ˉn<1⋯<n obtained from π by replacing every excedance π(i)>i by ¯π(i). Then the DEX set of π is the set of indices 1≤i<n such that ˉπ(i)>ˉπ(i+1). Finally, the DEX composition c1,…,ck of n corresponds to the DEX subset {c1,c1+c2,…,c1+⋯+ck−1}.
The (quasi)symmetric function
∑π∈Sλ,jFDEX(π),
where the sum is over the set of permutations of cycle type λ with j excedances, is the Eulerian quasisymmetric function.
Let π be a permutation in Sn. Let ˉπ be the word in the ordered set ˉ1<⋯<ˉn<1⋯<n obtained from π by replacing every excedance π(i)>i by ¯π(i). Then the DEX set of π is the set of indices 1≤i<n such that ˉπ(i)>ˉπ(i+1). Finally, the DEX composition c1,…,ck of n corresponds to the DEX subset {c1,c1+c2,…,c1+⋯+ck−1}.
The (quasi)symmetric function
∑π∈Sλ,jFDEX(π),
where the sum is over the set of permutations of cycle type λ with j excedances, is the Eulerian quasisymmetric function.
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.
Map
rotate front to back
Description
The front to back rotation of the entries of an integer composition.
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