Identifier
Values
[1,0] => [2,1] => [1,2] => [1,2] => 1
[1,0,1,0] => [3,1,2] => [1,3,2] => [1,3,2] => 2
[1,1,0,0] => [2,3,1] => [1,2,3] => [1,2,3] => 1
[1,0,1,0,1,0] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 3
[1,0,1,1,0,0] => [3,1,4,2] => [1,3,4,2] => [1,4,2,3] => 2
[1,1,0,0,1,0] => [2,4,1,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,1,0,1,0,0] => [4,3,1,2] => [1,4,2,3] => [1,3,4,2] => 2
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 1
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => 4
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,4,5,3,2] => [1,5,3,2,4] => 3
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,3,5,4,2] => [1,5,4,2,3] => 3
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [1,5,3,4,2] => [1,4,2,5,3] => 3
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,3,4,5,2] => [1,5,2,3,4] => 2
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => 3
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,2,4,5,3] => [1,2,5,3,4] => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [1,5,4,2,3] => [1,3,5,4,2] => 3
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [1,5,3,2,4] => [1,4,5,3,2] => 3
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,4,5,2,3] => [1,3,5,2,4] => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,2,5,3,4] => [1,2,4,5,3] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [1,5,2,3,4] => [1,3,4,5,2] => 2
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 5
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [1,5,6,4,3,2] => [1,6,4,3,2,5] => 4
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [1,4,6,5,3,2] => [1,6,5,3,2,4] => 4
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [1,6,4,5,3,2] => [1,5,3,2,6,4] => 4
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [1,4,5,6,3,2] => [1,6,3,2,4,5] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,3,6,5,4,2] => [1,6,5,4,2,3] => 4
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,3,5,6,4,2] => [1,6,4,2,3,5] => 3
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [1,6,5,3,4,2] => [1,4,2,6,5,3] => 4
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [1,6,4,2,3,5] => [1,3,5,6,4,2] => 3
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [1,5,6,3,4,2] => [1,4,2,6,3,5] => 3
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,3,4,6,5,2] => [1,6,5,2,3,4] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,3,6,4,5,2] => [1,5,2,3,6,4] => 3
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [1,6,3,4,5,2] => [1,5,2,4,6,3] => 3
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,2,5,6,4,3] => [1,2,6,4,3,5] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,2,4,6,5,3] => [1,2,6,5,3,4] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [1,2,6,4,5,3] => [1,2,5,3,6,4] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 2
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [1,6,5,4,2,3] => [1,3,6,5,4,2] => 4
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [1,5,6,4,2,3] => [1,3,6,4,2,5] => 3
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,6,5,3,2,4] => [1,4,6,5,3,2] => 4
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [1,5,3,2,6,4] => [1,6,4,5,3,2] => 4
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [1,5,6,3,2,4] => [1,4,6,3,2,5] => 3
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,4,6,5,2,3] => [1,3,6,5,2,4] => 3
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [1,6,4,5,2,3] => [1,3,5,2,6,4] => 3
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [1,6,3,2,4,5] => [1,4,5,6,3,2] => 3
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,4,5,6,2,3] => [1,3,6,2,4,5] => 2
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 2
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [1,2,6,5,3,4] => [1,2,4,6,5,3] => 3
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [1,2,6,4,3,5] => [1,2,5,6,4,3] => 3
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,2,5,6,3,4] => [1,2,4,6,3,5] => 2
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,6,5,2,3,4] => [1,3,4,6,5,2] => 3
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [1,6,4,2,3,5] => [1,3,5,6,4,2] => 3
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [1,6,3,4,2,5] => [1,4,2,5,6,3] => 3
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [1,5,6,2,3,4] => [1,3,4,6,2,5] => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [1,7,6,5,3,4,2] => [1,4,2,7,6,5,3] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [1,6,7,5,3,4,2] => [1,4,2,7,5,3,6] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [1,7,6,4,2,3,5] => [1,3,5,7,6,4,2] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [1,6,4,2,3,7,5] => [1,3,7,5,6,4,2] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [1,6,7,4,2,3,5] => [1,3,5,7,4,2,6] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [1,5,7,6,3,4,2] => [1,4,2,7,6,3,5] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [1,7,5,6,3,4,2] => [1,4,2,6,3,7,5] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [1,7,4,2,3,5,6] => [1,3,5,6,7,4,2] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [1,5,6,7,3,4,2] => [1,4,2,7,3,5,6] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [1,7,5,2,3,4,6] => [1,3,4,6,7,5,2] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [1,7,4,5,2,3,6] => [1,3,5,2,6,7,4] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [1,2,6,7,5,4,3] => [1,2,7,5,4,3,6] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [1,2,5,7,6,4,3] => [1,2,7,6,4,3,5] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [1,2,7,5,6,4,3] => [1,2,6,4,3,7,5] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [1,2,5,6,7,4,3] => [1,2,7,4,3,5,6] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [1,2,4,7,6,5,3] => [1,2,7,6,5,3,4] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [1,2,4,6,7,5,3] => [1,2,7,5,3,4,6] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [1,2,7,6,4,5,3] => [1,2,5,3,7,6,4] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [1,2,7,5,3,4,6] => [1,2,4,6,7,5,3] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [1,2,6,7,4,5,3] => [1,2,5,3,7,4,6] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [1,2,4,7,5,6,3] => [1,2,6,3,4,7,5] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [1,2,7,4,5,6,3] => [1,2,6,3,5,7,4] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [1,7,6,5,4,2,3] => [1,3,7,6,5,4,2] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [1,6,7,5,4,2,3] => [1,3,7,5,4,2,6] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [1,5,7,6,4,2,3] => [1,3,7,6,4,2,5] => 4
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [1,7,5,6,4,2,3] => [1,3,6,4,2,7,5] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [1,5,6,7,4,2,3] => [1,3,7,4,2,5,6] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [1,7,5,6,3,2,4] => [1,4,6,3,2,7,5] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [1,4,7,6,5,2,3] => [1,3,7,6,5,2,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [1,4,6,7,5,2,3] => [1,3,7,5,2,4,6] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [1,7,6,4,5,2,3] => [1,3,5,2,7,6,4] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [1,7,5,2,3,4,6] => [1,3,4,6,7,5,2] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [1,6,7,4,5,2,3] => [1,3,5,2,7,4,6] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [1,7,6,3,2,4,5] => [1,4,5,7,6,3,2] => 4
>>> Load all 153 entries. <<<
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [1,6,7,3,2,4,5] => [1,4,5,7,3,2,6] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,4,5,7,6,2,3] => [1,3,7,6,2,4,5] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,4,7,5,6,2,3] => [1,3,6,2,4,7,5] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [1,7,4,5,6,2,3] => [1,3,6,2,5,7,4] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [1,7,3,2,4,5,6] => [1,4,5,6,7,3,2] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,4,5,6,7,2,3] => [1,3,7,2,4,5,6] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [1,2,3,6,7,5,4] => [1,2,3,7,5,4,6] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [1,2,3,5,7,6,4] => [1,2,3,7,6,4,5] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [1,2,3,7,5,6,4] => [1,2,3,6,4,7,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [1,2,7,6,5,3,4] => [1,2,4,7,6,5,3] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [1,2,6,7,5,3,4] => [1,2,4,7,5,3,6] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [1,2,7,6,4,3,5] => [1,2,5,7,6,4,3] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [1,2,6,4,3,7,5] => [1,2,7,5,6,4,3] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [1,2,6,7,4,3,5] => [1,2,5,7,4,3,6] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [1,2,5,7,6,3,4] => [1,2,4,7,6,3,5] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [1,2,7,5,6,3,4] => [1,2,4,6,3,7,5] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [1,2,7,4,3,5,6] => [1,2,5,6,7,4,3] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [1,2,5,6,7,3,4] => [1,2,4,7,3,5,6] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [1,7,6,5,2,3,4] => [1,3,4,7,6,5,2] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [1,6,7,5,2,3,4] => [1,3,4,7,5,2,6] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [1,7,6,4,2,3,5] => [1,3,5,7,6,4,2] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [1,6,4,2,3,7,5] => [1,3,7,5,6,4,2] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [1,6,7,4,2,3,5] => [1,3,5,7,4,2,6] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [1,7,6,3,4,2,5] => [1,4,2,5,7,6,3] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [1,6,3,4,2,7,5] => [1,4,2,7,5,6,3] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [1,6,7,3,4,2,5] => [1,4,2,5,7,3,6] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [1,5,7,6,2,3,4] => [1,3,4,7,6,2,5] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [1,7,5,6,2,3,4] => [1,3,4,6,2,7,5] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [1,7,4,2,3,5,6] => [1,3,5,6,7,4,2] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [1,7,3,4,2,5,6] => [1,4,2,5,6,7,3] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [1,5,6,7,2,3,4] => [1,3,4,7,2,5,6] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [1,2,3,7,6,4,5] => [1,2,3,5,7,6,4] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [1,2,3,7,5,4,6] => [1,2,3,6,7,5,4] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [1,2,3,6,7,4,5] => [1,2,3,5,7,4,6] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [1,2,7,6,3,4,5] => [1,2,4,5,7,6,3] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [1,2,7,5,3,4,6] => [1,2,4,6,7,5,3] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [1,2,7,4,5,3,6] => [1,2,5,3,6,7,4] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [1,2,6,7,3,4,5] => [1,2,4,5,7,3,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,7,6,2,3,4,5] => [1,3,4,5,7,6,2] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [1,7,5,2,3,4,6] => [1,3,4,6,7,5,2] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [1,7,4,5,2,3,6] => [1,3,5,2,6,7,4] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [1,6,7,2,3,4,5] => [1,3,4,5,7,2,6] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
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Description
The number of cyclic descents of a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is given by the number of indices $1 \leq i \leq n$ such that $\pi(i) > \pi(i+1)$ where we set $\pi(n+1) = \pi(1)$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.