Identifier
Values
[1] => [1,0,1,0] => [1,2] => [2,1] => 2
[2] => [1,1,0,0,1,0] => [2,1,3] => [3,2,1] => 3
[1,1] => [1,0,1,1,0,0] => [1,3,2] => [2,1,3] => 1
[3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [4,3,2,1] => 4
[2,1] => [1,0,1,0,1,0] => [1,2,3] => [2,3,1] => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,3,4] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [5,4,3,2,1] => 5
[3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,4,2,1] => 3
[2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,2,1,4] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,1,3] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,1,3,4,5] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => 6
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,5,3,2,1] => 4
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [3,2,4,1] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,4,3,1] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [2,3,1,4] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [2,5,1,3,4] => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,1,3,4,5,6] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => 7
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,6,4,3,2,1] => 5
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,5,2,1] => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,5,4,2,1] => 4
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [4,3,2,1,5] => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [2,3,4,1] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [2,5,4,1,3] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,2,1,4,5] => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [2,4,1,3,5] => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [2,6,1,3,4,5] => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,1,3,4,5,6,7] => 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,2,1] => 8
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,4,6,3,2,1] => 4
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [4,6,5,3,2,1] => 5
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [4,3,2,5,1] => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [3,4,5,2,1] => 3
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [2,5,4,3,1] => 4
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,4,2,1,5] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2,5,1,4] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,4,5,1,3] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [2,6,5,1,3,4] => 3
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [2,3,1,4,5] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [2,5,1,3,4,6] => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [2,7,1,3,4,5,6] => 2
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,1,3,4,5,6,7,8] => 1
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [9,8,7,6,5,4,3,2,1] => 9
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,4,3,6,2,1] => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [4,5,6,3,2,1] => 4
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,6,5,4,2,1] => 5
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [5,4,3,2,1,6] => 1
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,4,2,5,1] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [3,2,5,4,1] => 3
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [2,4,5,3,1] => 3
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [2,6,5,4,1,3] => 4
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [3,2,4,1,5] => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,4,3,1,5] => 1
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [2,3,5,1,4] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [2,5,6,1,3,4] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [3,2,1,4,5,6] => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [2,4,1,3,5,6] => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [2,6,1,3,4,5,7] => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [2,8,1,3,4,5,6,7] => 2
[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] => [1,9,8,7,6,5,4,3,2] => [2,1,3,4,5,6,7,8,9] => 1
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [10,9,8,7,6,5,4,3,2,1] => 10
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [7,6,8,5,4,3,2,1] => 6
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [5,4,3,2,6,1] => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [4,5,3,6,2,1] => 3
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [4,3,6,5,2,1] => 4
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [3,5,6,4,2,1] => 4
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => 5
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [4,5,3,2,1,6] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [3,2,4,5,1] => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,4,3,5,1] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,3,5,4,1] => 3
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [2,5,6,4,1,3] => 3
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [4,3,2,1,5,6] => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [2,3,4,1,5] => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,5,4,1,3,6] => 1
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [3,2,6,1,4,5] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [2,4,6,1,3,5] => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [2,6,7,1,3,4,5] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [2,3,1,4,5,6] => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [2,5,1,3,4,6,7] => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [2,7,1,3,4,5,6,8] => 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] => [1,8,9,7,6,5,4,3,2] => [2,9,1,3,4,5,6,7,8] => 2
[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] => [1,10,9,8,7,6,5,4,3,2] => [2,1,3,4,5,6,7,8,9,10] => 1
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [6,5,4,3,2,1,7] => 1
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,5,3,2,6,1] => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,3,5,6,2,1] => 3
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,5,4,6,2,1] => 3
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,4,6,5,2,1] => 4
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [2,5,6,4,3,1] => 4
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,5,2,1,6] => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,5,4,2,1,6] => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,3,2,6,1,5] => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [2,3,4,5,1] => 2
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [2,5,4,6,1,3] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,6,5,1,4] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [2,4,6,5,1,3] => 3
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,4,2,1,5,6] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,5,1,4,6] => 1
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [2,4,5,1,3,6] => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [2,3,6,1,4,5] => 2
>>> Load all 247 entries. <<<
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [2,5,7,1,3,4,6] => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [2,7,8,1,3,4,5,6] => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [3,2,1,4,5,6,7] => 1
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [2,4,1,3,5,6,7] => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [2,6,1,3,4,5,7,8] => 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] => [1,7,9,8,6,5,4,3,2] => [2,8,1,3,4,5,6,7,9] => 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] => [1,9,10,8,7,6,5,4,3,2] => [2,10,1,3,4,5,6,7,8,9] => 2
[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] => [1,11,10,9,8,7,6,5,4,3,2] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[11] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [12,11,10,9,8,7,6,5,4,3,2,1] => 12
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [7,6,5,4,8,3,2,1] => 4
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [6,5,8,7,4,3,2,1] => 6
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [5,6,4,3,2,1,7] => 1
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,5,2,6,1] => 2
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,5,4,2,6,1] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [4,3,2,6,5,1] => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [3,4,5,6,2,1] => 3
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [2,5,4,6,3,1] => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,6,5,4,1] => 4
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [2,4,6,5,3,1] => 4
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [4,3,2,5,1,6] => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [3,4,5,2,1,6] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => 1
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,4,2,6,1,5] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,2,5,6,1,4] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,4,5,6,1,3] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [2,3,6,5,1,4] => 3
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,4,1,5,6] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [2,4,3,1,5,6] => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [2,3,5,1,4,6] => 1
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [2,3,1,4,5,6,7] => 1
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [7,6,5,4,3,2,1,8] => 1
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [5,4,6,3,2,1,7] => 1
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [4,6,5,3,2,1,7] => 1
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [4,3,2,5,6,1] => 2
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [3,4,5,2,6,1] => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,4,2,6,5,1] => 3
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,5,6,4,1] => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [2,4,5,6,3,1] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => 4
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [5,4,3,2,1,6,7] => 1
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,4,2,5,1,6] => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [2,4,5,3,1,6] => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,4,6,1,5] => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,4,3,6,1,5] => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [2,3,5,6,1,4] => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [4,3,2,1,5,6,7] => 1
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [2,3,4,1,5,6] => 1
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [3,2,1,4,5,6,7,8] => 1
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [7,6,5,4,3,2,8,1] => 2
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [6,5,7,4,8,3,2,1] => 4
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [6,7,5,4,3,2,1,8] => 1
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,4,3,6,2,1,7] => 1
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [4,5,6,3,2,1,7] => 1
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,6,5,4,2,1,7] => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,4,2,5,6,1] => 2
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [3,2,5,4,6,1] => 2
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [2,4,5,3,6,1] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [3,2,4,6,5,1] => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [2,3,5,6,4,1] => 3
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => 1
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 2
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [2,6,7,8,1,3,4,5] => 2
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [8,7,6,5,4,3,2,1,9] => 1
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [6,5,7,4,3,2,1,8] => 1
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [5,7,6,4,3,2,1,8] => 1
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [2,7,6,8,5,4,1,3] => 4
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [5,4,3,2,6,1,7] => 1
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [4,5,3,6,2,1,7] => 1
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [4,3,6,5,2,1,7] => 1
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [3,5,6,4,2,1,7] => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [2,6,5,4,3,1,7] => 1
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => 2
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => 2
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => 1
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [2,5,7,8,1,3,4,6] => 2
[2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [3,2,1,4,5,6,7,8,9] => 1
[7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,7,5,4,3,2,1,9,8] => [7,8,6,5,4,3,2,1,9] => 1
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [6,5,7,4,3,2,8,1] => 2
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [6,5,4,7,3,2,1,8] => 1
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [5,6,7,4,3,2,1,8] => 1
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [4,7,6,5,3,2,1,8] => 1
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [6,5,4,3,2,1,7,8] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 2
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [2,5,6,8,1,3,4,7] => 2
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [3,2,7,8,1,4,5,6] => 2
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [2,4,7,8,1,3,5,6] => 2
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [4,3,2,1,5,6,7,8] => 1
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [2,3,4,1,5,6,7] => 1
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [9,8,7,6,5,4,3,2,1,10] => 1
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [5,4,3,2,1,6,7,8] => 1
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [2,3,4,7,1,5,6] => 2
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [2,4,6,8,1,3,5,7] => 2
[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] => [2,1,10,9,8,7,6,5,4,3] => [3,2,1,4,5,6,7,8,9,10] => 1
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [6,5,4,3,7,2,8,1] => 2
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,5,2,6,7,1] => 2
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [3,4,5,6,2,7,1] => 2
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [5,4,3,2,8,1,6,7] => 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] => [2,3,5,6,7,1,4] => 2
[] => [] => [] => [] => 0
[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] => [2,3,4,5,6,7,1] => 2
[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] => [2,3,4,5,6,1,7] => 1
[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] => [2,3,4,5,7,1,6] => 2
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [2,3,4,5,1,6,7] => 1
[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] => [2,3,4,6,7,1,5] => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [3,2,4,5,6,7,1] => 2
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,4,2,5,6,7,1] => 2
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [3,4,5,2,6,7,1] => 2
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [4,3,2,5,6,7,1] => 2
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => 2
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,1,8] => 1
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 2
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [2,3,4,5,6,1,7,8] => 1
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [2,3,4,5,7,8,1,6] => 2
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [2,3,4,5,1,6,7,8] => 1
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [3,2,4,5,6,7,8,1] => 2
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [3,2,7,6,5,4,1,8] => 1
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,4,2,5,6,7,8,1] => 2
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [3,4,5,2,6,7,8,1] => 2
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [4,3,2,5,6,7,8,1] => 2
[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [4,3,2,1,5,6,7,8,9] => 1
[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [4,3,2,1,5,6,7,8,9,10] => 1
[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [5,4,3,2,1,6,7,8,9] => 1
[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] => [4,3,2,1,10,9,8,7,6,5] => [5,4,3,2,1,6,7,8,9,10] => 1
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [6,5,4,3,2,1,7,8,9] => 1
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [7,6,5,4,3,2,1,8,9,10] => 1
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [7,6,5,4,3,2,1,8,9] => 1
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [8,7,6,5,4,3,2,1,9,10] => 1
[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] => [1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,1] => 2
[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,1,9] => 1
[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,7,9,1,8] => 2
[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] => [1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,1] => 2
[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,1,10] => 1
[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [2,3,4,5,6,7,1,8,9] => 1
[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] => [2,1,3,4,5,6,7,8,9] => [3,2,4,5,6,7,8,9,1] => 2
[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,4,2,5,6,7,8,9,1] => 2
[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] => [2,1,3,4,5,6,7,8,9,10] => [3,2,4,5,6,7,8,9,10,1] => 2
[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] => [5,4,3,2,1,10,9,8,7,6] => [6,5,4,3,2,1,7,8,9,10] => 1
[9,9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [10,9,8,7,6,5,4,3,2,1,11] => 1
[5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,5,4,3,2] => [2,7,8,9,10,1,3,4,5,6] => 2
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Description
The number of saliances of the permutation.
A saliance is a right-to-left maximum. This can be described as an occurrence of the mesh pattern $([1], {(1,1)})$, i.e., the upper right quadrant is shaded, see [1].
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.