Identifier
Values
[1,0] => [1,0] => [1] => [1] => 1
[1,0,1,0] => [1,1,0,0] => [2,1] => [2,1] => 2
[1,1,0,0] => [1,0,1,0] => [1,2] => [1,2] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3,2,1] => [3,2,1] => 3
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [2,3,1] => [2,3,1] => 2
[1,1,0,0,1,0] => [1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 2
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => [1,3,2] => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,2,3] => [1,3,2] => 2
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => 4
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [3,4,2,1] => [3,4,2,1] => 3
[1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => 3
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,4,3,1] => 3
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,4,3,1] => 3
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => 3
[1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,4,1,3] => 2
[1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => 3
[1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,3,2] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => 3
[1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,4,3] => 3
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,4,3,2] => 3
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,4,3,2] => 3
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,4,3,2] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [3,5,4,2,1] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,5,4,2,1] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [3,5,2,4,1] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2,5,4,1] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,5,4,3,1] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [2,5,4,3,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,5,4,1] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [2,5,4,3,1] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [2,5,4,3,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,5,4,3,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [3,5,2,1,4] => 3
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,5,1,4] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [2,5,4,1,3] => 3
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,5,4,1,3] => 3
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,5,4] => 4
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,5,1,4,3] => 3
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,4,3] => 4
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,4,3,2] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,4,3,2] => 4
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => 4
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,4,3,2] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,4,3,2] => 4
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,5,4] => 4
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,5,1,4,3] => 3
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,5,4,3] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,5,4,3,2] => 4
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,5,4,3,2] => 4
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,5,4,3] => 4
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,5,4,3,2] => 4
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,5,4,3,2] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,5,4,3,2] => 4
[1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,5,4,3] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,5,4,3,2] => 4
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,5,4,3,2] => 4
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,5,4,3,2] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,5,4,3,2] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [4,6,5,3,2,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [4,6,5,3,2,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [4,6,3,5,2,1] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [4,3,6,5,2,1] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [3,6,5,4,2,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [3,6,5,4,2,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,6,5,2,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [3,6,5,4,2,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [3,6,5,4,2,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [3,6,5,4,2,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [4,6,3,2,5,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [4,3,6,2,5,1] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [3,6,5,2,4,1] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,6,5,4,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,6,5,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => 5
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,6,5,4,1] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [4,6,3,2,1,5] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [4,3,6,2,1,5] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [3,6,5,2,1,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,6,5,2,1,4] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,6,1,5] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [2,6,5,4,1,3] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,6,5,1,4] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,6,1,5,4] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [2,6,5,1,4,3] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [2,6,1,5,4,3] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,5,4,3] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,6,5,4] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,5,4,3] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,5,4,3,2] => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,6,5] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [3,6,2,1,5,4] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,6,1,5,4] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,6,5,4] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,6,5,4,3] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,6,5,4,3,2] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,6,5,4,3,2] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,6,5,4,3,2] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,6,5,4,3,2] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,6,5,4] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,6,5,4,3] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,6,5,4,3,2] => 5
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,6,5,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,6,5,4,3,2] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 5
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Description
The width of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The width of the tree is given by the number of leaves of this tree.
Note that, due to the construction of this tree, the width of the tree is always one more than the number of descents St000021The number of descents of a permutation.. This also matches the number of runs in a permutation St000470The number of runs in a permutation..
See also St000308The height of the tree associated to a permutation. for the height of this tree.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).