Identifier
Values
[1,0,1,0] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => 2
[1,0,1,0,1,0] => [2,3,1] => [3,2,1] => 2
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => 2
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,2,3,1] => 3
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => 3
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4,2,1,3] => 3
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => 3
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => 3
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [4,1,3,2] => 3
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4,3,2,1] => 2
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,2,4] => 3
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => 3
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5,2,3,4,1] => 4
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => 4
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => 3
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => 4
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => 4
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => 3
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => 3
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [5,2,1,4,3] => 4
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [5,2,4,3,1] => 3
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,2,1,3,5] => 4
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => 3
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,5,3,4] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => 4
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => 4
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [5,1,3,4,2] => 4
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [4,1,3,2,5] => 4
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [5,3,2,4,1] => 3
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5,4,3,2,1] => 3
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [4,3,2,1,5] => 3
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,1,2,5,4] => 3
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [5,1,3,2,4] => 4
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [5,3,2,1,4] => 3
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,1,2,4,5] => 4
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => 4
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,5,2,4,3] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,5,4,3,2] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => 4
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [5,1,2,4,3] => 4
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [5,1,4,3,2] => 3
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5,4,2,3,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [4,1,2,3,5] => 4
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => 4
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => 4
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5,1,2,3,4] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [6,2,3,1,5,4] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [6,2,1,4,5,3] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [5,2,1,4,3,6] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [6,2,4,3,5,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6,2,5,4,3,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,2,4,3,1,6] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [6,2,1,4,3,5] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [6,2,4,3,1,5] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,6,3,5,4] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [6,2,1,3,5,4] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [6,2,1,5,4,3] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6,2,5,3,4,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => 5
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 4
>>> Load all 261 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,6,3,2,5,4] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,6,3,5,4,2] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [6,1,3,4,5,2] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [5,1,3,4,2,6] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [4,1,3,2,6,5] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [6,1,3,4,2,5] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,1,3,2,5,6] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [5,3,2,4,1,6] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [6,3,2,4,1,5] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6,4,3,2,1,5] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [6,1,3,2,5,4] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [6,1,3,5,4,2] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [5,1,3,2,4,6] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [6,3,2,1,5,4] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [6,3,2,5,4,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [6,5,3,2,4,1] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [5,3,2,1,4,6] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [6,1,3,2,4,5] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [6,3,2,1,4,5] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,6,2,4,5,3] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,5,2,4,3,6] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,6,4,3,5,2] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,6,5,4,3,2] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,6,2,4,3,5] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,6,4,3,2,5] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [6,1,2,4,5,3] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [5,1,2,4,3,6] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [6,1,4,3,5,2] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [6,1,5,4,3,2] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [5,1,4,3,2,6] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [6,4,2,3,5,1] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [6,5,2,4,3,1] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [5,4,2,3,1,6] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [6,1,2,4,3,5] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [6,1,4,3,2,5] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6,4,2,3,1,5] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,6,3,5,4] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,6,2,3,5,4] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,6,2,5,4,3] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,6,5,3,4,2] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [6,1,2,3,5,4] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [6,1,2,5,4,3] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [6,1,5,3,4,2] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [6,5,2,3,4,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,7,4,6,5] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,6,5,4] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,7,4,3,6,5] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,7,4,6,5,3] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,7,3,5,6,4] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,6,3,5,4,7] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,7,5,4,6,3] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,7,6,5,4,3] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,7,3,5,4,6] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,7,5,4,3,6] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,7,4,6,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,7,3,4,6,5] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,7,3,6,5,4] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,6,4,5,3] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 7
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Description
The number of weak deficiencies of a permutation.
This is defined as
$$\operatorname{wdec}(\sigma)=\#\{i:\sigma(i) \leq i\}.$$
The number of weak exceedances is St000213The number of weak exceedances (also weak excedences) of a permutation., the number of deficiencies is St000703The number of deficiencies of a permutation..
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.