Identifier
Values
[1] => [1,0,1,0] => [2,1] => 0
[2] => [1,1,0,0,1,0] => [3,1,2] => 0
[1,1] => [1,0,1,1,0,0] => [2,3,1] => 0
[3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 0
[2,1] => [1,0,1,0,1,0] => [2,1,3] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 0
[4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0
[3,1] => [1,1,0,1,0,0,1,0] => [3,1,2,4] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 0
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 0
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => 0
[3,2] => [1,1,0,0,1,0,1,0] => [3,1,4,2] => 1
[3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,3,4] => 0
[2,2,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => 0
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 0
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => 0
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => 0
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => 0
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => 0
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 0
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => 0
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => 1
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => 0
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => 1
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => 0
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => 1
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => 0
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => 0
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => 0
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => 0
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 1
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => 0
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => 0
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => 1
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => 1
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => 0
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => 0
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => 1
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => 0
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 0
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => 0
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => 0
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => 0
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 1
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => 0
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => 1
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => 0
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => 1
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => 2
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => 1
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => 1
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => 0
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => 1
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => 0
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 0
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => 1
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => 1
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => 2
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => 0
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => 1
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => 0
[1,1,1,1,1,1,1,1,1] => [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] => 0
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => 0
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 1
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9] => 0
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => 1
>>> Load all 282 entries. <<<
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => 0
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => 1
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => 2
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => 1
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 1
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => 0
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 0
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => 1
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => 0
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => 0
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => 2
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => 1
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => 1
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => 0
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => 0
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => 2
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => 0
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 0
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => 1
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,9,1,8] => 1
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => 0
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
[10,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => 0
[9,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 1
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 1
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => 1
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 1
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => 0
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => 1
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => 1
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => 1
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => 1
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => 1
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 1
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => 1
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => 0
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => 2
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => 1
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => 1
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => 2
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 0
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => 0
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => 2
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => 0
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => 1
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => 1
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => 1
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => 3
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => 1
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 2
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => 1
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => 3
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => 0
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => 2
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => 1
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => 2
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => 2
[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => 1
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => 1
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => 0
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => 2
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => 2
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => 1
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => 1
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => 2
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => 1
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => 3
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => 3
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => 3
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => 2
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => 2
[8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => 0
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => 1
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => 1
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => 1
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => 2
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => 4
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => 0
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => 1
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => 0
[7,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6,9] => 0
[6,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => 1
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => 2
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => 0
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => 1
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => 2
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => 1
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => 2
[9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 0
[8,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6,9] => 1
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => 1
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => 4
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => 1
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => 1
[] => [] => [] => 0
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => 6
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => 3
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => 4
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => 4
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => 4
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => 5
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => 4
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => 2
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => 4
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => 4
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => 1
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => 2
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => 5
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => 4
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => 4
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => 0
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => 5
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => 4
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => 2
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => 5
[4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => 2
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => 4
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => 4
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => 4
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => 1
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => 4
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => 3
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 0
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 0
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => 0
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 0
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => 8
[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 0
[7,7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => 1
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Description
The number of boxed occurrences of 132 in a permutation.
This is the number of occurrences of the pattern $132$ such that any entry between the three matched entries is either larger than the largest matched entry or smaller than the smallest matched entry.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.