Identifier
Values
[1,0] => [1] => [1] => [1] => 1
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 2
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 3
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [3,2,1] => 1
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [3,1,2] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 3
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [1,4,2,3] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,3,2,1] => [4,3,2,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,4,2,1] => [4,3,1,2] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => 3
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,4,3,1] => [4,1,3,2] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,2,3,1] => [4,2,3,1] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,2,4,1] => [4,2,1,3] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,3,4] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,5,3,2] => [1,5,4,2,3] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,2,3,5] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,3,5,4,2] => [1,5,2,4,3] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,3,4,2] => [1,5,3,4,2] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,4,3,5,2] => [1,5,3,2,4] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => [2,1,5,3,4] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,5,3,2,1] => [5,4,3,1,2] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,4,2,1,5] => [4,3,1,2,5] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,5,4,2,1] => [5,4,1,3,2] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,3,4,2,1] => [5,4,2,3,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,3,5,2,1] => [5,4,2,1,3] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => 4
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => [3,1,2,5,4] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,4,3,1,5] => [4,1,3,2,5] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,5,4,3,1] => [5,1,4,3,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,4,5,3,1] => [5,1,4,2,3] => 3
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,2,3,1,5] => [4,2,3,1,5] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,4,2,3,1] => [5,3,4,2,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,2,4,3,1] => [5,2,4,3,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [4,2,5,3,1] => [5,2,4,1,3] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [3,2,4,1,5] => [4,2,1,3,5] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2,5,4,1] => [5,2,1,4,3] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,3,2,4,1] => [5,3,2,4,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [3,5,2,4,1] => [5,3,1,4,2] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [3,4,2,5,1] => [5,3,1,2,4] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,6,4,3] => [1,2,6,5,3,4] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,4,6,5,3] => [1,2,6,3,5,4] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,6,4,5,3] => [1,2,6,4,5,3] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,2,6,4,3,5] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,6,4,3,2] => [1,6,5,4,2,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,5,3,2,6] => [1,5,4,2,3,6] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,4,6,5,3,2] => [1,6,5,2,4,3] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,4,5,3,2] => [1,6,5,3,4,2] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,5,4,6,3,2] => [1,6,5,3,2,4] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,3,5,4,2,6] => [1,5,2,4,3,6] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,3,6,5,4,2] => [1,6,2,5,4,3] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,3,5,6,4,2] => [1,6,2,5,3,4] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,5,3,4,2,6] => [1,5,3,4,2,6] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,3,4,2] => [1,6,4,5,3,2] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,3,5,4,2] => [1,6,3,5,4,2] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,5,3,6,4,2] => [1,6,3,5,2,4] => 3
>>> Load all 227 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,5,3,2,4,6] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,4,3,6,5,2] => [1,6,3,2,5,4] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,4,3,5,2] => [1,6,4,3,5,2] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,4,6,3,5,2] => [1,6,4,2,5,3] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,6,4,2,3,5] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,4,6,5,3] => [2,1,6,3,5,4] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,4,5,3] => [2,1,6,4,5,3] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [2,1,6,4,3,5] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,6,5,3,2,1] => [6,5,4,1,3,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,4,5,3,2,1] => [6,5,4,2,3,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,5,4,2,1,6] => [5,4,1,3,2,6] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,6,5,4,2,1] => [6,5,1,4,3,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,5,6,4,2,1] => [6,5,1,4,2,3] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,3,4,2,1,6] => [5,4,2,3,1,6] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,3,5,4,2,1] => [6,5,2,4,3,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [5,3,6,4,2,1] => [6,5,2,4,1,3] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,4,3,5,2,1] => [6,5,3,2,4,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [4,6,3,5,2,1] => [6,5,3,1,4,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,4,3,1,5,6] => [4,1,3,2,5,6] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,4,3,1,6,5] => [4,1,3,2,6,5] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,5,4,3,1,6] => [5,1,4,3,2,6] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,6,5,4,3,1] => [6,1,5,4,3,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [2,5,6,4,3,1] => [6,1,5,4,2,3] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [2,4,5,3,1,6] => [5,1,4,2,3,6] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [2,4,6,5,3,1] => [6,1,5,2,4,3] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [2,6,4,5,3,1] => [6,1,5,3,4,2] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,5,4,6,3,1] => [6,1,5,3,2,4] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,2,3,1,5,6] => [4,2,3,1,5,6] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [4,2,3,1,6,5] => [4,2,3,1,6,5] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,4,2,3,1,6] => [5,3,4,2,1,6] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,5,4,2,3,1] => [6,4,5,3,2,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [5,6,4,2,3,1] => [6,4,5,3,1,2] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,2,4,3,1,6] => [5,2,4,3,1,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,5,2,4,3,1] => [6,3,5,4,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,2,5,4,3,1] => [6,2,5,4,3,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [5,2,6,4,3,1] => [6,2,5,4,1,3] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [4,2,5,3,1,6] => [5,2,4,1,3,6] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [4,2,6,5,3,1] => [6,2,5,1,4,3] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,4,2,5,3,1] => [6,3,5,2,4,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [4,6,2,5,3,1] => [6,3,5,1,4,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [4,5,2,6,3,1] => [6,3,5,1,2,4] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [4,2,1,3,6,5] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,5,4,1,6] => [5,2,1,4,3,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,2,6,5,4,1] => [6,2,1,5,4,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,5,6,4,1] => [6,2,1,5,3,4] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,3,2,4,1,6] => [5,3,2,4,1,6] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,5,3,2,4,1] => [6,4,3,5,2,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,3,2,5,4,1] => [6,3,2,5,4,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [5,3,2,6,4,1] => [6,3,2,5,1,4] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [3,5,2,4,1,6] => [5,3,1,4,2,6] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [3,6,5,2,4,1] => [6,4,1,5,3,2] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [3,6,2,5,4,1] => [6,3,1,5,4,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,3,5,2,4,1] => [6,4,2,5,3,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [5,3,6,2,4,1] => [6,4,2,5,1,3] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,4,2,6,5,1] => [6,3,1,2,5,4] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [3,6,4,2,5,1] => [6,4,1,3,5,2] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,3,4,2,5,1] => [6,4,2,3,5,1] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [4,3,6,2,5,1] => [6,4,2,1,5,3] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [5,3,4,2,1,6,7] => [5,4,2,3,1,6,7] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [4,6,3,5,2,1,7] => [6,5,3,1,4,2,7] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [7,4,5,3,6,2,1] => [7,6,4,2,3,5,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6,7] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [5,4,2,3,1,6,7] => [5,3,4,2,1,6,7] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6,7] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [3,5,2,4,1,6,7] => [5,3,1,4,2,6,7] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [6,3,4,2,5,1,7] => [6,4,2,3,5,1,7] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [7,6,3,4,2,5,1] => [7,5,3,4,6,2,1] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [4,3,6,2,5,1,7] => [6,4,2,1,5,3,7] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [7,4,3,5,2,6,1] => [7,5,3,2,4,6,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [4,7,3,5,2,6,1] => [7,5,3,1,4,6,2] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [4,5,3,7,2,6,1] => [7,5,3,1,2,6,4] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => 4
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searching the database for statistics with the same generating function
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Description
The height 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 statistic is given by the height of this tree.
See also St000325The width of the tree associated to a permutation. for the width of this tree.
Map
inverse
Description
Sends a permutation to its inverse.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
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.).