Identifier
Values
[1,0] => [1] => ([],1) => 1
[1,0,1,0] => [2,1] => ([(0,1)],2) => 0
[1,1,0,0] => [1,2] => ([],2) => 2
[1,0,1,0,1,0] => [2,1,3] => ([(1,2)],3) => 1
[1,0,1,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => 0
[1,1,0,0,1,0] => [3,1,2] => ([(0,2),(1,2)],3) => 0
[1,1,0,1,0,0] => [1,3,2] => ([(1,2)],3) => 1
[1,1,1,0,0,0] => [1,2,3] => ([],3) => 3
[1,0,1,0,1,0,1,0] => [2,1,4,3] => ([(0,3),(1,2)],4) => 0
[1,0,1,0,1,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 0
[1,0,1,1,0,0,1,0] => [2,1,3,4] => ([(2,3)],4) => 2
[1,0,1,1,0,1,0,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 0
[1,1,0,0,1,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 0
[1,1,0,1,0,0,1,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => 1
[1,1,0,1,0,1,0,0] => [1,3,2,4] => ([(2,3)],4) => 2
[1,1,0,1,1,0,0,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => 1
[1,1,1,0,1,0,0,0] => [1,2,4,3] => ([(2,3)],4) => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => 4
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => 1
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 0
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => 0
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 1
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 0
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => ([(3,4)],5) => 3
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => 1
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 1
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 0
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => 0
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 1
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => ([(3,4)],5) => 3
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 1
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => 1
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => ([(3,4)],5) => 3
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 1
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => ([(3,4)],5) => 3
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6) => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => ([(4,5)],6) => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => ([(4,5)],6) => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => ([(4,5)],6) => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => ([(4,5)],6) => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => ([(4,5)],6) => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([],6) => 6
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Description
The number of isolated vertices of a graph.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.