Identifier
Values
[1] => [1,0,1,0] => [2,1] => [1,2] => 0
[2] => [1,1,0,0,1,0] => [3,1,2] => [1,3,2] => 1
[1,1] => [1,0,1,1,0,0] => [2,3,1] => [2,1,3] => 1
[3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => 2
[2,1] => [1,0,1,0,1,0] => [2,1,3] => [2,3,1] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => 3
[3,1] => [1,1,0,1,0,0,1,0] => [3,1,2,4] => [2,4,3,1] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => [3,2,4,1] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => 3
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 4
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [2,5,4,3,1] => 3
[3,2] => [1,1,0,0,1,0,1,0] => [3,1,4,2] => [2,4,1,3] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,3,4] => [3,4,2,1] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => [3,1,4,2] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [4,3,2,5,1] => 3
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 4
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 5
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => 4
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [2,5,4,1,3] => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [3,5,4,2,1] => 3
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [3,4,1,2] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [4,3,5,2,1] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,3,1,5,2] => 3
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => 4
[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] => [6,5,4,3,2,1,7] => 5
[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] => [1,8,7,6,5,4,3,2] => 6
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [2,6,5,4,1,3] => 4
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => 4
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [2,5,1,4,3] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [3,5,4,1,2] => 3
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [4,5,3,2,1] => 3
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [3,2,5,1,4] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [4,3,5,1,2] => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => 4
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [4,2,1,5,3] => 3
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [5,4,3,1,6,2] => 4
[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] => [7,6,5,4,3,2,1,8] => 6
[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] => [1,9,8,7,6,5,4,3,2] => 7
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [2,6,5,1,4,3] => 4
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [3,6,5,4,1,2] => 4
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => 4
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => 3
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [3,5,1,4,2] => 3
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [3,5,2,1,4] => 3
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [4,5,3,1,2] => 3
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => 4
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [3,2,5,4,1] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [4,1,5,3,2] => 3
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [4,2,5,1,3] => 3
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [5,4,3,6,1,2] => 4
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => 3
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [5,4,2,1,6,3] => 4
[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] => [7,6,5,4,3,2,8,1] => 6
[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] => [8,7,6,5,4,3,2,1,9] => 7
[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] => [1,10,9,8,7,6,5,4,3,2] => 8
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [2,6,1,5,4,3] => 4
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [3,6,5,1,4,2] => 4
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [3,6,5,2,1,4] => 4
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [4,6,5,3,1,2] => 4
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => 4
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [3,1,6,5,4,2] => 3
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [3,5,2,4,1] => 3
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [4,5,1,3,2] => 3
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [4,5,2,1,3] => 3
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [5,4,6,3,1,2] => 4
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [4,2,5,3,1] => 3
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [5,4,1,6,3,2] => 4
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [4,3,2,6,1,5] => 3
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [5,4,2,6,1,3] => 4
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [5,3,2,1,6,4] => 4
[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] => [9,8,7,6,5,4,3,2,1,10] => 8
[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] => [1,11,10,9,8,7,6,5,4,3,2] => 9
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => 4
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [3,6,1,5,4,2] => 4
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [3,6,5,2,4,1] => 4
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => 4
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [4,6,5,2,1,3] => 4
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 4
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => 3
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [4,1,6,5,3,2] => 3
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [3,2,6,1,5,4] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [4,5,2,3,1] => 3
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [5,4,6,1,3,2] => 4
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [4,3,6,2,1,5] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => 4
[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] => [7,6,5,4,8,3,2,1] => 6
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => 3
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,4,2,6,3,1] => 4
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [5,3,2,6,1,4] => 4
[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] => [5,4,3,2,1,7,6] => 4
[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] => [10,9,8,7,6,5,4,3,2,1,11] => 9
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [3,6,2,5,4,1] => 4
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [4,6,1,5,3,2] => 4
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [3,6,2,1,5,4] => 4
>>> Load all 185 entries. <<<
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [4,6,5,2,3,1] => 4
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [5,6,4,1,3,2] => 4
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [4,6,3,2,1,5] => 4
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [5,6,4,2,1,3] => 4
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [3,2,6,5,1,4] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [4,2,6,5,3,1] => 3
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [5,1,6,4,3,2] => 4
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => 3
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [4,3,6,2,5,1] => 3
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [5,4,6,2,3,1] => 4
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [5,3,6,2,1,4] => 4
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => 4
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,3,2,6,4,1] => 4
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [7,6,5,3,2,1,8,4] => 6
[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] => [2,1,8,7,6,5,4,3] => 5
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [7,6,8,5,4,3,2,1] => 6
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [4,6,2,5,3,1] => 4
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [5,6,1,4,3,2] => 4
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [4,6,2,1,5,3] => 4
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [4,6,3,2,5,1] => 4
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [5,6,4,2,3,1] => 4
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [5,6,3,2,1,4] => 4
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [4,2,6,5,1,3] => 3
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [5,2,6,4,3,1] => 4
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [4,3,6,1,5,2] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [5,2,6,1,4,3] => 4
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [5,3,6,2,4,1] => 4
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => 4
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [6,4,3,2,7,1,5] => 5
[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] => [6,5,4,3,2,1,8,7] => 5
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => 4
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,6,3,5,2,1] => 4
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [5,6,2,4,3,1] => 4
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [4,6,3,1,5,2] => 4
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => 4
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [5,6,3,2,4,1] => 4
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [5,2,6,4,1,3] => 4
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [5,3,6,4,2,1] => 4
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => 4
[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] => [3,8,1,7,6,5,4,2] => 6
[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] => [4,8,7,1,6,5,3,2] => 6
[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] => [5,8,7,6,1,4,3,2] => 6
[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] => [6,8,7,5,4,1,3,2] => 6
[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] => [7,8,6,5,4,3,1,2] => 6
[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] => [7,6,8,5,4,2,1,3] => 6
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [4,6,3,5,1,2] => 4
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [5,6,2,4,1,3] => 4
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [5,6,3,4,2,1] => 4
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [5,6,3,1,4,2] => 4
[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] => [7,6,5,8,3,2,1,4] => 6
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [5,3,6,4,1,2] => 4
[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] => [7,6,4,3,8,2,1,5] => 6
[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] => [7,5,4,3,2,8,1,6] => 6
[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] => [3,2,1,8,7,6,5,4] => 4
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 4
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [5,4,3,2,1,8,7,6] => 4
[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] => [2,1,10,9,8,7,6,5,4,3] => 7
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [7,8,6,5,4,2,3,1] => 6
[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] => [4,3,2,1,8,7,6,5] => 3
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [7,6,2,1,8,5,4,3] => 6
[3,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,9,3] => [8,6,5,4,3,2,9,1,7] => 7
[2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [8,7,6,5,4,3,2,1,10,9] => 7
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [5,3,8,7,6,4,2,1] => 5
[6,6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [6,2,8,7,5,4,3,1] => 5
[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] => [7,1,8,6,5,4,3,2] => 6
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [6,4,7,2,5,1,3] => 5
[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] => [7,8,5,6,3,4,1,2] => 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] => [7,5,3,1,8,6,4,2] => 6
[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] => [7,5,3,8,2,6,1,4] => 6
[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] => [7,5,8,6,2,4,1,3] => 6
[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] => [7,4,8,2,6,5,1,3] => 6
[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] => [6,5,8,7,3,4,1,2] => 5
[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] => [6,8,5,7,3,1,4,2] => 6
[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] => [6,5,8,7,4,3,2,1] => 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] => [6,4,8,3,7,5,1,2] => 5
[4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [6,5,4,3,2,1,10,9,8,7] => 5
[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] => [4,3,2,1,10,9,8,7,6,5] => 5
[10,10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 9
[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [8,6,9,4,7,2,5,1,3] => 7
[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] => [9,10,7,8,5,6,3,4,1,2] => 8
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Description
The maximum drop size of a permutation.
The maximum drop size of a permutation $\pi$ of $[n]=\{1,2,\ldots, n\}$ is defined to be the maximum value of $i-\pi(i)$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.