Identifier
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => 1
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,1,3,2] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [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] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,2,4,1] => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,3,4,1] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,4,3,1] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,4,2,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,5,3,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,1,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,5,4,2] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,1,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,1,3,5,2] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [5,1,3,4,2] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,1,4,3,2] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,5,3,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [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
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [3,2,4,1,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [3,2,4,5,1] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,2,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [5,2,3,4,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,2,4,3,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,3,4,1,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,3,4,5,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,3,5,4,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,4,3,1,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,5,3,4,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,5,4,3,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [3,4,2,1,5] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,4,2,5,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,5,2,4,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,5,4,2,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [4,5,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[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
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,5,3,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,5,3,6,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,6,3,5,4] => 2
[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
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[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
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,5,4,6,3] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,6,4,5,3] => 2
[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
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,4,5,6,3] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,4,6,5,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,5,6,4,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,1,2,4,6,5] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,1,2,5,4,6] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,1,2,5,6,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,1,2,6,5,4] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,1,4,2,6,5] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [3,1,4,6,5,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,5,4,2,6] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,1,5,4,6,2] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,6,4,5,2] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,1,6,5,4,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,1,3,2,5,6] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,1,3,2,6,5] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,1,3,5,2,6] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,3,5,6,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [4,1,3,6,5,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [5,1,3,4,2,6] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [5,1,3,4,6,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [6,1,3,4,5,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [6,1,3,5,4,2] => 2
>>> Load all 228 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,1,4,3,2,6] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [6,1,4,3,5,2] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [6,1,4,5,3,2] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,1,5,4,3,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[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
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,5,3,4,6] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,5,3,6,4] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,6,3,5,4] => 3
[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
[1,1,0,0,1,1,0,0,1,1,0,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,5,4,6,3] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,4,5,3] => 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
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,4,5,6,3] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,1,4,6,5,3] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,5,6,4,3] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,5,6,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,6,5,4] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [3,2,4,1,5,6] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [3,2,4,1,6,5] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [3,2,4,5,1,6] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [3,2,4,5,6,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [3,2,4,6,5,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,2,5,4,1,6] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [3,2,5,4,6,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [3,2,6,4,5,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [3,2,6,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,2,3,1,6,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,2,3,6,5,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [5,2,3,4,1,6] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [5,2,3,4,6,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [6,2,3,4,5,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [6,2,3,5,4,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,2,4,3,1,6] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,2,4,3,6,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [6,2,4,3,5,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [6,2,4,5,3,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,2,5,4,3,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,5,6,4] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,6,5,4] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,3,4,1,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,3,4,1,6,5] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,3,4,5,1,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,3,4,5,6,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [2,3,4,6,5,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [2,3,5,4,1,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [2,3,5,4,6,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [2,3,6,4,5,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,3,6,5,4,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,4,3,1,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,4,3,1,6,5] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,4,3,5,1,6] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,4,3,5,6,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [2,4,3,6,5,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,5,3,4,1,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,5,3,4,6,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,6,3,4,5,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,6,3,5,4,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,5,4,3,1,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [2,5,4,3,6,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,6,4,3,5,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [2,6,4,5,3,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,6,5,4,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,4,2,1,5,6] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,4,2,1,6,5] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,4,2,5,1,6] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,4,2,5,6,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,4,2,6,5,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,5,2,4,1,6] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,5,2,4,6,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,6,2,4,5,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [3,6,2,5,4,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,5,4,2,1,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,5,4,2,6,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,6,4,2,5,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,6,4,5,2,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [3,6,5,4,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [4,5,3,2,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [4,5,3,2,6,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [4,6,3,2,5,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [4,6,3,5,2,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [5,6,3,4,2,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [5,6,4,3,2,1] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,1,2,4,5,7,6] => 2
[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] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,7,5,6] => 2
[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] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [3,2,4,5,6,7,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,2,3,4,6,7,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [6,2,3,4,5,7,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [6,2,4,5,3,1,7] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,2,5,4,3,1,7] => 2
[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] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [2,3,4,1,5,7,6] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [2,3,4,5,1,6,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [2,3,4,5,1,7,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [2,3,4,5,6,1,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [2,3,4,5,6,7,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,6,5,4,3,1,7] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [3,4,2,5,6,7,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,6,5,4,2,1,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [5,6,4,3,2,1,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,7,6,8,5] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,5,4,6,3,8,7] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => 1
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Description
The number of left outer peaks of a permutation.
A left outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $1$ if $w_1 > w_2$.
In other words, it is a peak in the word $[0,w_1,..., w_n]$.
This appears in [1, def.3.1]. The joint distribution with St000366The number of double descents of a permutation. is studied in [3], where left outer peaks are called exterior peaks.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Alexandersson Kebede
Description
Sends a permutation to a permutation and it preserves the set of right-to-left minima.
Take a permutation $\pi$ of length $n$. The mapping looks for a smallest odd integer $i\in[n-1]$ such that swapping the entries $\pi(i)$ and $\pi(i+1)$ preserves the set of right-to-left minima. Otherwise, $\pi$ will be a fixed element of the mapping. Note that the map changes the sign of all non-fixed elements.
There are exactly $\binom{\lfloor n/2 \rfloor}{k-\lceil n/2 \rceil}$ elements in $S_n$ fixed under this map, with exactly $k$ right-to-left minima, see Lemma 35 in [1].