Identifier
Values
[1,0] => [1] => [1] => ([],1) => 2
[1,0,1,0] => [1,2] => [2,1] => ([],2) => 3
[1,1,0,0] => [2,1] => [1,2] => ([(0,1)],2) => 4
[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => ([],3) => 4
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => ([(1,2)],3) => 5
[1,1,0,0,1,0] => [2,1,3] => [3,1,2] => ([(1,2)],3) => 5
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => ([(0,1),(0,2)],3) => 6
[1,1,1,0,0,0] => [3,1,2] => [2,1,3] => ([(0,2),(1,2)],3) => 6
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => ([],4) => 5
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,4,2,1] => ([(2,3)],4) => 6
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4) => 6
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,3,1] => ([(1,2),(1,3)],4) => 7
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [3,2,4,1] => ([(1,3),(2,3)],4) => 7
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [4,3,1,2] => ([(2,3)],4) => 6
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => ([(0,3),(1,2)],4) => 7
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [4,1,3,2] => ([(1,2),(1,3)],4) => 7
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4) => 8
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4) => 8
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [4,2,1,3] => ([(1,3),(2,3)],4) => 7
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 8
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4) => 9
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 8
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => ([],5) => 6
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => ([(3,4)],5) => 7
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,3,4,2,1] => ([(3,4)],5) => 7
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,4,2,1] => ([(2,3),(2,4)],5) => 8
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 8
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,4,2,3,1] => ([(3,4)],5) => 7
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 8
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5) => 8
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5) => 9
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5) => 9
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 8
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5) => 9
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5) => 10
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 9
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => ([(3,4)],5) => 7
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 8
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 8
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5) => 9
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 9
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [5,4,1,3,2] => ([(2,3),(2,4)],5) => 8
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5) => 9
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5) => 9
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5) => 10
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5) => 10
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5) => 9
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5) => 10
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 11
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5) => 10
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 8
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 9
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5) => 9
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5) => 10
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 10
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 10
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [2,5,1,4,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 11
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 12
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 11
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 9
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [3,5,2,1,4] => ([(0,4),(1,4),(2,3),(2,4)],5) => 10
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [3,2,5,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 11
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 12
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => ([],6) => 7
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(4,5)],6) => 8
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(4,5)],6) => 8
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => ([(3,4),(3,5)],6) => 9
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 9
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(4,5)],6) => 8
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 9
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => ([(3,4),(3,5)],6) => 9
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => ([(2,3),(2,4),(2,5)],6) => 10
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [5,3,6,4,2,1] => ([(2,5),(3,4),(3,5)],6) => 10
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 9
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [4,6,3,5,2,1] => ([(2,5),(3,4),(3,5)],6) => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [4,3,6,5,2,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => 11
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 10
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => ([(4,5)],6) => 8
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 9
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 9
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 10
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => ([(3,4),(3,5)],6) => 9
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6) => 10
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6) => 11
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [6,4,2,5,3,1] => ([(2,5),(3,4),(3,5)],6) => 10
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 9
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => ([(2,5),(3,4),(3,5)],6) => 10
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [5,3,6,2,4,1] => ([(1,5),(2,4),(3,4),(3,5)],6) => 11
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6) => 11
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [5,3,2,6,4,1] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 10
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [4,3,6,2,5,1] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 13
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 11
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => ([(4,5)],6) => 8
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 10
>>> Load all 213 entries. <<<
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 9
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 10
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [5,3,6,4,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 11
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [4,6,3,5,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 11
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 11
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => ([(3,4),(3,5)],6) => 9
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => ([(0,4),(0,5),(1,2),(1,3)],6) => 11
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6) => 10
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6) => 11
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 12
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [6,5,3,1,4,2] => ([(2,5),(3,4),(3,5)],6) => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [5,6,3,1,4,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => 11
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 12
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [3,6,1,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 13
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 11
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6) => 10
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [5,6,2,4,1,3] => ([(0,5),(1,3),(2,4),(2,5)],6) => 11
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [6,4,2,5,1,3] => ([(1,5),(2,4),(3,4),(3,5)],6) => 11
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 12
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [5,4,2,6,1,3] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 12
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => ([(2,4),(2,5),(3,4),(3,5)],6) => 11
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 15
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [6,4,2,1,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 10
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 11
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [5,3,6,2,1,4] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 12
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [6,3,2,5,1,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 13
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 13
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 13
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 16
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 11
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [4,3,2,6,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 15
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 12
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 14
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => ([],8) => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [7,8,5,6,4,3,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [6,5,8,7,4,3,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8) => 13
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [7,8,6,4,5,3,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [8,6,7,4,5,3,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [8,5,4,7,6,3,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8) => 13
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [7,8,6,5,3,4,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [8,6,7,5,3,4,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [8,7,5,6,3,4,2,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [6,8,7,3,5,4,2,1] => ([(2,6),(2,7),(3,4),(3,5)],8) => 13
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,3,8,5] => [5,8,3,7,6,4,2,1] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 15
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [7,6,8,4,3,5,2,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 13
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [8,7,4,3,6,5,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8) => 13
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [4,3,8,7,6,5,2,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 17
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [7,5,4,8,3,6,2,1] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 15
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [6,5,4,3,8,7,2,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 17
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [7,8,6,5,4,2,3,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [8,6,7,5,4,2,3,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [8,7,5,6,4,2,3,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [8,7,6,4,5,2,3,1] => ([(4,7),(5,6)],8) => 11
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [8,5,7,6,2,4,3,1] => ([(2,6),(2,7),(3,4),(3,5)],8) => 13
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [8,4,7,2,6,5,3,1] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 15
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [7,6,8,5,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 13
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [8,6,5,7,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [8,7,6,3,2,5,4,1] => ([(4,6),(4,7),(5,6),(5,7)],8) => 13
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [8,3,2,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 17
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [8,6,4,3,7,2,5,1] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 15
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [8,5,4,3,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 17
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [7,8,6,5,4,3,1,2] => ([(4,7),(5,6)],8) => 11
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [8,6,7,5,4,3,1,2] => ([(4,7),(5,6)],8) => 11
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [8,7,5,6,4,3,1,2] => ([(4,7),(5,6)],8) => 11
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [8,7,6,4,5,3,1,2] => ([(4,7),(5,6)],8) => 11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8) => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8) => 13
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [6,5,8,7,3,4,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => 15
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [6,8,7,5,4,1,3,2] => ([(2,6),(2,7),(3,4),(3,5)],8) => 13
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [8,5,7,6,4,1,3,2] => ([(2,6),(2,7),(3,4),(3,5)],8) => 13
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [8,7,4,6,5,1,3,2] => ([(2,6),(2,7),(3,4),(3,5)],8) => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [5,8,7,6,1,4,3,2] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4)],8) => 15
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [4,8,7,1,6,5,3,2] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7)],8) => 17
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [7,5,8,6,3,1,4,2] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => 15
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => [6,8,5,7,3,1,4,2] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => 15
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [8,7,3,6,1,5,4,2] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 15
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [3,8,1,7,6,5,4,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7)],8) => 19
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [6,8,4,3,7,1,5,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6)],8) => 17
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => [5,8,4,3,1,7,6,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 19
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [7,6,8,5,4,2,1,3] => ([(2,7),(3,7),(4,6),(5,6)],8) => 13
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => [7,5,8,6,2,4,1,3] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => 15
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [6,8,5,7,2,4,1,3] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8) => 15
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [7,4,8,2,6,5,1,3] => ([(0,5),(1,4),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => 17
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => ([(4,6),(4,7),(5,6),(5,7)],8) => 13
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [7,8,5,6,2,1,4,3] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) => 15
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8) => 17
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8) => 21
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) => 19
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => [5,4,8,2,1,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7)],8) => 21
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [7,6,5,8,3,2,1,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => 15
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => [7,3,2,8,6,5,1,4] => ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 19
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [8,7,5,3,2,6,1,4] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 15
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => [6,3,2,8,7,1,5,4] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 21
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 23
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [7,6,4,3,8,2,1,5] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8) => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 17
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => 25
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [7,5,4,3,2,8,1,6] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 19
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => 21
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Description
The number of chains of a poset.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.