Identifier
Values
[1] => [1,0,1,0] => [1,2] => [1,2] => 1
[2] => [1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 1
[1,1] => [1,0,1,1,0,0] => [1,3,2] => [1,3,2] => 0
[3] => [1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,3,1,4] => 1
[2,1] => [1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,3,4,2] => 0
[4] => [1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,3,4,1,5] => 1
[3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => 1
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => 0
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,4,1,2,5] => 2
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 0
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => 2
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [2,4,1,3,5] => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [3,1,4,2,5] => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,3,1,5,4] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 3
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,3,5,2,4] => 1
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => 0
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,2,5,3] => 0
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 1
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 0
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [2,4,5,1,3,6] => 2
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,3,1,4,5] => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => 3
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,3,4,2,5] => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => 1
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => 1
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 0
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,3,5,1,4,6] => 2
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => 3
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => 1
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => 3
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [1,3,5,6,7,2,4] => 1
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => 0
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 0
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => 0
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => 3
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => 1
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,1,5,2,3,6] => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 1
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [3,4,1,2,6,5] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 3
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [1,3,4,6,7,2,5] => 1
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => 0
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => 0
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,5,6,3,4] => 1
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 1
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => 0
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => 3
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [2,5,1,3,4,6] => 3
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [3,1,5,2,4,6] => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [4,1,2,5,3,6] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,3,4,5,7,2,6] => 1
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => 0
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 4
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => 1
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => 1
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => 0
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [1,3,5,6,2,7,4] => 0
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => 0
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 1
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => 3
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 1
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 4
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 1
>>> Load all 241 entries. <<<
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [1,4,5,7,2,3,6] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 0
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 3
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [1,3,6,7,2,4,5] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,4,6,2,7,3,5] => 1
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 0
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 1
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 1
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 3
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 4
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 3
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [1,3,5,7,2,4,6] => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [1,4,5,2,7,3,6] => 1
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 0
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 1
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [1,3,4,6,2,7,5] => 0
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 1
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 3
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,4,2,6,7,3,5] => 1
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [1,3,5,2,6,7,4] => 0
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 2
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [1,3,5,6,2,4,7] => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 4
[5,4,2,2] => [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
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 3
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [1,3,4,7,2,5,6] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 1
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 3
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [1,4,2,5,7,3,6] => 1
[4,4,3,2] => [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
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 1
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [1,4,6,2,3,7,5] => 1
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 3
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [1,3,6,2,7,4,5] => 1
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,4,6,7,3,5] => 2
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => 1
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [1,3,4,6,2,5,7] => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => 0
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 4
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 3
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [1,3,5,2,7,4,6] => 1
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [1,2,4,5,7,3,6] => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 3
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [1,3,6,2,4,7,5] => 1
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [1,4,2,6,3,7,5] => 0
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => 3
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => 0
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => 1
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 2
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [1,4,6,2,3,5,7] => 3
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [1,3,5,2,6,4,7] => 1
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 2
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [1,4,5,2,3,7,6] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 5
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [1,3,7,2,4,5,6] => 3
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [1,4,2,7,3,5,6] => 2
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [1,2,5,7,3,4,6] => 3
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => 0
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,4,6,3,7,5] => 1
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [1,3,2,6,7,4,5] => 1
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => 2
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 2
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => 3
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [1,3,6,2,4,5,7] => 3
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [1,4,2,6,3,5,7] => 2
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => 3
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [1,3,5,2,4,7,6] => 1
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [1,4,2,5,3,7,6] => 0
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,5,6] => 1
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [1,2,4,7,3,5,6] => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,5,7,4,6] => 1
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [1,2,5,3,7,4,6] => 2
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,2,3,6,7,5] => 1
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,4,7,5] => 0
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [1,2,6,3,4,7,5] => 2
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 3
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [1,3,5,2,4,6,7] => 3
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => 1
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [1,2,4,6,3,5,7] => 3
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => 1
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [1,2,5,3,6,4,7] => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => 1
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => 2
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => 2
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 4
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [1,2,3,5,7,4,6] => 3
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => 1
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => 1
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => 2
[6,5,4,3,2,1] => [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] => 6
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 4
[6,4,4,3,2,1] => [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] => 4
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 4
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 3
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 4
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 2
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 4
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 4
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 3
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 4
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 2
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 2
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => 2
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 4
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => 2
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => 4
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 3
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 4
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 2
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 2
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => 2
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 2
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 0
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => 2
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 4
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => 2
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => 2
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 3
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Description
The number of ascent tops in the permutation such that all smaller elements appear before.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
inverse
Description
Sends a permutation to its inverse.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.