Identifier
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [1,2] => 0
[1,1,0,0] => [1,2] => [2,1] => 1
[1,0,1,0,1,0] => [2,1,3] => [3,1,2] => 1
[1,0,1,1,0,0] => [2,3,1] => [2,1,3] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => 1
[1,1,0,1,0,0] => [1,3,2] => [2,3,1] => 1
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 2
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [3,4,1,2] => 1
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,1,4,3] => 2
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [4,3,1,2] => 2
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [4,2,1,3] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => 2
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [1,3,2,4] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,1,4,2] => 2
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [4,1,3,2] => 2
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [4,2,3,1] => 2
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [3,2,4,1] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => 2
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [2,4,3,1] => 2
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [3,4,2,1] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => 3
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => 2
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [5,2,1,4,3] => 3
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [4,3,5,1,2] => 2
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [2,1,4,3,5] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [4,2,1,5,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [3,5,4,1,2] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [2,1,5,4,3] => 3
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [4,5,3,1,2] => 2
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [4,5,2,1,3] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [3,2,1,5,4] => 3
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => 3
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [5,4,2,1,3] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [5,3,2,1,4] => 3
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => 3
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [5,1,3,2,4] => 2
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [5,3,1,4,2] => 3
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [4,1,3,2,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [3,1,4,2,5] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [4,3,1,5,2] => 3
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [1,3,2,5,4] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => 3
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [4,5,1,3,2] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => 2
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [3,2,5,4,1] => 3
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [5,4,1,3,2] => 3
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [5,4,2,3,1] => 3
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [5,3,2,4,1] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [4,3,2,5,1] => 3
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [1,4,2,5,3] => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,1,5,3,2] => 3
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [1,4,3,5,2] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [2,4,3,5,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [4,2,5,3,1] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [5,1,4,3,2] => 3
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [5,2,4,3,1] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [5,3,4,2,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [4,3,5,2,1] => 3
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => 3
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [2,5,4,3,1] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [3,5,4,2,1] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => 3
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [5,6,2,1,4,3] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [4,3,6,5,1,2] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [2,1,4,3,6,5] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [4,2,1,6,5,3] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [6,5,2,1,4,3] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,4,3,5,1,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [6,2,1,4,3,5] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [6,4,2,1,5,3] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [5,4,3,6,1,2] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [5,2,1,4,3,6] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [4,2,1,5,3,6] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [5,4,2,1,6,3] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [3,5,4,6,1,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [2,1,5,4,6,3] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [5,3,6,4,1,2] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [2,1,5,3,6,4] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [6,3,5,4,1,2] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [6,2,1,5,4,3] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [6,4,5,2,1,3] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [6,3,2,1,5,4] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [5,4,6,3,1,2] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [3,2,1,5,4,6] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [5,3,2,1,6,4] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [3,6,5,4,1,2] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [2,1,6,5,4,3] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [4,6,5,3,1,2] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [4,6,5,2,1,3] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [3,2,1,6,5,4] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [5,6,4,2,1,3] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [5,6,3,2,1,4] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [4,3,2,1,6,5] => 4
>>> Load all 206 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [6,5,4,2,1,3] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [6,5,3,2,1,4] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [6,4,3,2,1,5] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [5,6,1,3,2,4] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [5,6,3,1,4,2] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [4,1,3,2,6,5] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [3,1,4,2,6,5] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [6,5,1,3,2,4] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [6,5,3,1,4,2] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [6,4,1,3,2,5] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [6,3,1,4,2,5] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [6,4,3,1,5,2] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [5,4,1,3,2,6] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [5,3,1,4,2,6] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [4,3,1,5,2,6] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [5,4,3,1,6,2] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [1,3,2,5,4,6] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [3,1,5,4,6,2] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [5,1,3,2,6,4] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [5,3,1,6,4,2] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [6,1,3,2,5,4] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [6,3,1,5,4,2] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [6,4,5,1,3,2] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [6,3,2,5,4,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [5,4,6,1,3,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [5,4,6,2,3,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [3,2,5,4,6,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [5,3,2,6,4,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,3,2,6,5,4] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [3,1,6,5,4,2] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [4,6,5,2,3,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [3,2,6,5,4,1] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [5,6,4,1,3,2] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [5,6,3,2,4,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [4,3,2,6,5,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [6,5,4,1,3,2] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [6,5,3,2,4,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [5,4,3,2,6,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [1,4,2,5,3,6] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [4,1,5,3,6,2] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [5,1,4,2,6,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [4,1,5,2,6,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,4,1,6,3,2] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [6,1,4,2,5,3] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [6,4,1,5,3,2] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [6,1,4,3,5,2] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [6,2,4,3,5,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [6,4,2,5,3,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [5,1,4,3,6,2] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [5,2,4,3,6,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [4,2,5,3,6,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [5,4,2,6,3,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [1,4,2,6,5,3] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [4,1,6,5,3,2] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [1,4,3,6,5,2] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [2,4,3,6,5,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [4,2,6,5,3,1] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [5,6,1,4,3,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [5,6,2,4,3,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [4,3,6,5,2,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [6,5,1,4,3,2] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [6,5,2,4,3,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [6,4,3,5,2,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [5,4,3,6,2,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [1,5,2,6,4,3] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [5,1,6,4,3,2] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [1,5,3,6,4,2] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [2,5,3,6,4,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [5,2,6,4,3,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [1,5,4,6,3,2] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [2,5,4,6,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [3,5,4,6,2,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [5,3,6,4,2,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [6,1,5,4,3,2] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [6,3,5,4,2,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [5,4,6,3,2,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [2,6,5,4,3,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [3,6,5,4,2,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [4,6,5,3,2,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [1,3,2,5,4,7,6] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [1,3,2,6,4,7,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [1,3,2,6,5,7,4] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,3,2,7,6,5,4] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [1,4,2,5,3,7,6] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [1,4,2,6,3,7,5] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [1,4,2,6,5,7,3] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [1,4,3,6,5,7,2] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [1,4,2,7,6,5,3] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [1,4,3,7,6,5,2] => 4
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The maximum of the number of descents and the number of inverse descents.
This is, the maximum of St000021The number of descents of a permutation. and St000354The number of recoils of a permutation..
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
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.