Identifier
Values
[1,0] => [2,1] => [2,1] => [1] => 0
[1,0,1,0] => [3,1,2] => [2,3,1] => [2,1] => 0
[1,1,0,0] => [2,3,1] => [3,1,2] => [1,2] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [2,3,4,1] => [2,3,1] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [2,4,1,3] => [2,1,3] => 0
[1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2] => [3,1,2] => 0
[1,1,0,1,0,0] => [4,3,1,2] => [3,4,2,1] => [3,2,1] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4] => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [2,4,1,5,3] => [2,4,1,3] => 0
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [2,4,5,3,1] => [2,4,3,1] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [2,5,1,3,4] => [2,1,3,4] => 0
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,1,4,5,2] => [3,1,4,2] => 0
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4] => [3,1,2,4] => 0
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,1] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,2,1] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,5,2,1,4] => [3,2,1,4] => 1
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [4,1,2,5,3] => [4,1,2,3] => 0
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,1,5,3,2] => [4,1,3,2] => 1
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,5,2,3,1] => [4,2,3,1] => 2
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => [2,3,5,1,4] => 0
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => [2,3,5,4,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => [2,3,1,4,5] => 0
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => [2,4,1,5,3] => 0
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => [2,4,1,3,5] => 0
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => [2,4,5,3,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => [2,4,5,3,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [2,4,6,3,1,5] => [2,4,3,1,5] => 1
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => [2,5,1,3,4] => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => [2,5,1,4,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [2,5,6,3,4,1] => [2,5,3,4,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => [2,1,3,4,5] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => [3,1,4,5,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => [3,1,4,2,5] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => [3,1,5,2,4] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [3,1,5,6,4,2] => [3,1,5,4,2] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => [3,1,2,4,5] => 0
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,4,2,6,1,5] => [3,4,2,1,5] => 1
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => [3,4,5,1,2] => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [3,4,6,2,1,5] => [3,4,2,1,5] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => [3,5,2,1,4] => 1
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => [3,5,2,4,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [3,5,6,2,4,1] => [3,5,2,4,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,6,2,1,4,5] => [3,2,1,4,5] => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => [4,1,2,5,3] => 0
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => [4,1,2,3,5] => 0
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => [4,1,5,3,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,1,5,6,3,2] => [4,1,5,3,2] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,1,6,3,2,5] => [4,1,3,2,5] => 1
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,5,2,3,6,1] => [4,5,2,3,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => [4,5,2,3,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [4,5,3,2,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,6,2,3,1,5] => [4,2,3,1,5] => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => [5,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,1,2,6,4,3] => [5,1,2,4,3] => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,1,6,3,4,2] => [5,1,3,4,2] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,6,2,3,4,1] => [5,2,3,4,1] => 3
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6] => [2,3,4,5,1,6] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5] => [2,3,4,6,1,5] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [2,3,4,6,7,5,1] => [2,3,4,6,5,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6] => [2,3,4,1,5,6] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4] => [2,3,5,1,6,4] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6] => [2,3,5,1,4,6] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [2,3,5,6,4,7,1] => [2,3,5,6,4,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [2,3,5,6,7,4,1] => [2,3,5,6,4,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [2,3,5,7,4,1,6] => [2,3,5,4,1,6] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5] => [2,3,6,1,4,5] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [2,3,6,1,7,5,4] => [2,3,6,1,5,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [2,3,6,7,4,5,1] => [2,3,6,4,5,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6] => [2,3,1,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3] => [2,4,1,5,6,3] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6] => [2,4,1,5,3,6] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5] => [2,4,1,6,3,5] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [2,4,1,6,7,5,3] => [2,4,1,6,5,3] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6] => [2,4,1,3,5,6] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [2,4,5,3,6,7,1] => [2,4,5,3,6,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [2,4,5,3,7,1,6] => [2,4,5,3,1,6] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [2,4,5,6,3,7,1] => [2,4,5,6,3,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => [2,4,5,6,1,3] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [2,4,5,7,3,1,6] => [2,4,5,3,1,6] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [2,4,6,3,1,7,5] => [2,4,6,3,1,5] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [2,4,6,3,7,5,1] => [2,4,6,3,5,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [2,4,6,7,3,5,1] => [2,4,6,3,5,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [2,4,7,3,1,5,6] => [2,4,3,1,5,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4] => [2,5,1,3,6,4] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6] => [2,5,1,3,4,6] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [2,5,1,6,4,7,3] => [2,5,1,6,4,3] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [2,5,1,6,7,4,3] => [2,5,1,6,4,3] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [2,5,1,7,4,3,6] => [2,5,1,4,3,6] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [2,5,6,3,4,7,1] => [2,5,6,3,4,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [2,5,6,3,7,4,1] => [2,5,6,3,4,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [2,5,6,7,4,3,1] => [2,5,6,4,3,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [2,5,7,3,4,1,6] => [2,5,3,4,1,6] => 2
>>> Load all 231 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5] => [2,6,1,3,4,5] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [2,6,1,3,7,5,4] => [2,6,1,3,5,4] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [2,6,1,7,4,5,3] => [2,6,1,4,5,3] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [2,6,7,3,4,5,1] => [2,6,3,4,5,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2] => [3,1,4,5,6,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6] => [3,1,4,5,2,6] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => [3,1,4,6,2,5] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [3,1,4,6,7,5,2] => [3,1,4,6,5,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6] => [3,1,4,2,5,6] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => [3,1,5,2,6,4] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6] => [3,1,5,2,4,6] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [3,1,5,6,4,7,2] => [3,1,5,6,4,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [3,1,5,6,7,4,2] => [3,1,5,6,4,2] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [3,1,5,7,4,2,6] => [3,1,5,4,2,6] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5] => [3,1,6,2,4,5] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [3,1,6,2,7,5,4] => [3,1,6,2,5,4] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [3,1,6,7,4,5,2] => [3,1,6,4,5,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6] => [3,1,2,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [3,4,2,5,7,1,6] => [3,4,2,5,1,6] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [3,4,2,6,1,7,5] => [3,4,2,6,1,5] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [3,4,2,6,7,5,1] => [3,4,2,6,5,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [3,4,2,7,1,5,6] => [3,4,2,1,5,6] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [3,4,5,2,7,1,6] => [3,4,5,2,1,6] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => [3,4,5,6,1,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [3,4,5,7,1,2,6] => [3,4,5,1,2,6] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [3,4,6,2,1,7,5] => [3,4,6,2,1,5] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [3,4,6,2,7,5,1] => [3,4,6,2,5,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [3,4,6,7,1,5,2] => [3,4,6,1,5,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [3,4,7,2,1,5,6] => [3,4,2,1,5,6] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [3,5,2,1,6,7,4] => [3,5,2,1,6,4] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [3,5,2,1,7,4,6] => [3,5,2,1,4,6] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [3,5,2,6,4,7,1] => [3,5,2,6,4,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [3,5,2,6,7,4,1] => [3,5,2,6,4,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [3,5,2,7,4,1,6] => [3,5,2,4,1,6] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [3,5,6,2,4,7,1] => [3,5,6,2,4,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [3,5,6,2,7,4,1] => [3,5,6,2,4,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [3,5,6,7,4,1,2] => [3,5,6,4,1,2] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [3,5,7,2,4,1,6] => [3,5,2,4,1,6] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [3,6,2,1,4,7,5] => [3,6,2,1,4,5] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [3,6,2,1,7,5,4] => [3,6,2,1,5,4] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [3,6,2,7,4,5,1] => [3,6,2,4,5,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [3,6,7,2,4,5,1] => [3,6,2,4,5,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [3,7,2,1,4,5,6] => [3,2,1,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3] => [4,1,2,5,6,3] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6] => [4,1,2,5,3,6] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5] => [4,1,2,6,3,5] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [4,1,2,6,7,5,3] => [4,1,2,6,5,3] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6] => [4,1,2,3,5,6] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [4,1,5,3,6,7,2] => [4,1,5,3,6,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [4,1,5,3,7,2,6] => [4,1,5,3,2,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [4,1,5,6,3,7,2] => [4,1,5,6,3,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [4,1,5,6,7,2,3] => [4,1,5,6,2,3] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [4,1,5,7,3,2,6] => [4,1,5,3,2,6] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [4,1,6,3,2,7,5] => [4,1,6,3,2,5] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [4,1,6,3,7,5,2] => [4,1,6,3,5,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [4,1,6,7,3,5,2] => [4,1,6,3,5,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [4,1,7,3,2,5,6] => [4,1,3,2,5,6] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [4,5,2,3,7,1,6] => [4,5,2,3,1,6] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [4,5,2,6,3,7,1] => [4,5,2,6,3,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [4,5,2,6,7,1,3] => [4,5,2,6,1,3] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [4,5,2,7,3,1,6] => [4,5,2,3,1,6] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,5,6,3,7,1,2] => [4,5,6,3,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [4,5,6,7,3,1,2] => [4,5,6,3,1,2] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [4,5,7,3,2,1,6] => [4,5,3,2,1,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [4,6,2,3,1,7,5] => [4,6,2,3,1,5] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [4,6,2,3,7,5,1] => [4,6,2,3,5,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [4,6,2,7,3,5,1] => [4,6,2,3,5,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,6,7,3,2,5,1] => [4,6,3,2,5,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [4,7,2,3,1,5,6] => [4,2,3,1,5,6] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4] => [5,1,2,3,6,4] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6] => [5,1,2,3,4,6] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [5,1,2,6,4,7,3] => [5,1,2,6,4,3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [5,1,2,6,7,4,3] => [5,1,2,6,4,3] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [5,1,2,7,4,3,6] => [5,1,2,4,3,6] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [5,1,6,3,4,7,2] => [5,1,6,3,4,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [5,1,6,3,7,4,2] => [5,1,6,3,4,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [5,1,6,7,4,3,2] => [5,1,6,4,3,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [5,1,7,3,4,2,6] => [5,1,3,4,2,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [5,6,2,3,4,7,1] => [5,6,2,3,4,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [5,6,2,3,7,4,1] => [5,6,2,3,4,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [5,6,2,7,4,3,1] => [5,6,2,4,3,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [5,7,2,3,4,1,6] => [5,2,3,4,1,6] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5] => [6,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [6,1,2,3,7,5,4] => [6,1,2,3,5,4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [6,1,2,7,4,5,3] => [6,1,2,4,5,3] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [6,1,7,3,4,5,2] => [6,1,3,4,5,2] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [6,7,2,3,4,5,1] => [6,2,3,4,5,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,6,8,1,7] => [2,3,4,5,6,1,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [2,3,4,5,7,1,8,6] => [2,3,4,5,7,1,6] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [2,3,4,5,8,1,6,7] => [2,3,4,5,1,6,7] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [2,3,4,8,1,5,6,7] => [2,3,4,1,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [2,3,5,6,7,8,1,4] => [2,3,5,6,7,1,4] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [3,1,8,2,4,5,6,7] => [3,1,2,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [4,5,6,3,2,8,1,7] => [4,5,6,3,2,1,7] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [5,1,2,3,6,7,8,4] => [5,1,2,3,6,7,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [5,1,2,3,8,4,6,7] => [5,1,2,3,4,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [6,1,2,3,4,7,8,5] => [6,1,2,3,4,7,5] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [7,1,2,3,4,5,8,6] => [7,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [2,3,4,5,6,7,9,1,8] => [2,3,4,5,6,7,1,8] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [2,9,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,1,2] => [3,4,5,6,7,8,1,2] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [7,1,2,3,4,5,8,9,6] => [7,1,2,3,4,5,8,6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [8,1,2,3,4,5,6,9,7] => [8,1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [9,1,2,3,4,5,6,7,10,8] => [9,1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [2,10,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [8,1,2,3,4,5,6,9,10,7] => [8,1,2,3,4,5,6,9,7] => 0
[] => [1] => [1] => [] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,8,10,1,9] => [2,3,4,5,6,7,8,1,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,9,11,1,10] => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
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Description
The number of mid points of decreasing subsequences of length 3 in a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the number of indices $j$ such that there exist indices $i,k$ with $i < j < k$ and $\pi(i) > \pi(j) > \pi(k)$. In other words, this is the number of indices that are neither left-to-right maxima nor right-to-left minima.
This statistic can also be expressed as the number of occurrences of the mesh pattern ([3,2,1], {(0,2),(0,3),(2,0),(3,0)}): the shading fixes the first and the last element of the decreasing subsequence.
See also St000119The number of occurrences of the pattern 321 in a permutation..
Map
inverse
Description
Sends a permutation to its inverse.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.