Identifier
Values
[1] => [1,0,1,0] => [2,1] => 1
[2] => [1,1,0,0,1,0] => [3,1,2] => 1
[1,1] => [1,0,1,1,0,0] => [2,3,1] => 1
[3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[2,1] => [1,0,1,0,1,0] => [3,2,1] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 1
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 1
[3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 1
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 1
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 2
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 1
[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] => 1
[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
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => 1
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 2
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 1
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 2
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 1
[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] => 1
[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
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => 2
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 2
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 1
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 1
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 2
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => 2
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => 1
[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] => 1
[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
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => 1
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => 2
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => 1
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => 2
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => 2
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => 1
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 2
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 1
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => 1
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 3
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 2
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 2
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => 1
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 2
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 2
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => 2
[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] => [3,2,4,5,6,7,8,9,1] => 1
[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] => 1
[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
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => 1
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => 2
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => 1
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => 2
>>> Load all 254 entries. <<<
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => 2
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => 1
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => 2
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => 2
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => 2
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => 1
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 2
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 1
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 2
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => 2
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => 1
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 3
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 2
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => 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] => [4,2,3,5,6,7,8,9,1] => 1
[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] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => 2
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => 2
[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] => [3,4,2,5,6,7,8,9,1] => 2
[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] => [3,2,4,5,6,7,8,9,10,1] => 1
[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] => 1
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 2
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 3
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 2
[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
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 3
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 3
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 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] => 3
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 3
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 2
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 3
[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] => 2
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 3
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 2
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 3
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 2
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => 3
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 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] => 2
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 3
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 3
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 3
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => 2
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 3
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 3
[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
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 3
[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
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => 3
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 3
[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
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => 3
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => 2
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 3
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 3
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => 3
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 3
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 3
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 3
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 3
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 4
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => 4
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 4
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 3
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => 3
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 4
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 4
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => 3
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => 2
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => 4
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 4
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 4
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 4
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 2
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => 4
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => 4
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => 3
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => 3
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 4
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => 3
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => 3
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 4
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 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] => 4
[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
[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] => 3
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => 3
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => 3
[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] => 3
[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] => [9,8,7,6,5,4,3,2,1] => 4
[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] => [10,9,8,7,6,5,4,3,2,1] => 5
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => 4
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => 5
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => 4
[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] => 5
[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => 5
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => 4
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => 4
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => 4
[9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => 5
[9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => 5
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The Elizalde-Pak rank of a permutation.
This is the largest $k$ such that $\pi(i) > k$ for all $i\leq k$.
According to [1], the length of the longest increasing subsequence in a $321$-avoiding permutation is equidistributed with the rank of a $132$-avoiding permutation.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.