Identifier
Values
[1] => [1] => [[1]] => 0
[1,1] => [1,1] => [[1,1]] => 0
[1,2] => [1,2] => [[1,2]] => 1
[2,1] => [1,2] => [[1,2]] => 1
[1,1,1] => [1,1,1] => [[1,1,1]] => 0
[1,1,2] => [1,1,2] => [[1,1,2]] => 1
[1,2,1] => [1,1,2] => [[1,1,2]] => 1
[2,1,1] => [1,1,2] => [[1,1,2]] => 1
[1,1,3] => [1,1,3] => [[1,1,3]] => 2
[1,3,1] => [1,1,3] => [[1,1,3]] => 2
[3,1,1] => [1,1,3] => [[1,1,3]] => 2
[1,2,2] => [1,2,2] => [[1,2,2]] => 2
[2,1,2] => [1,2,2] => [[1,2,2]] => 2
[2,2,1] => [1,2,2] => [[1,2,2]] => 2
[1,2,3] => [1,2,3] => [[1,2,3]] => 3
[1,3,2] => [1,2,3] => [[1,2,3]] => 3
[2,1,3] => [1,2,3] => [[1,2,3]] => 3
[2,3,1] => [1,2,3] => [[1,2,3]] => 3
[3,1,2] => [1,2,3] => [[1,2,3]] => 3
[3,2,1] => [1,2,3] => [[1,2,3]] => 3
[1,1,1,1] => [1,1,1,1] => [[1,1,1,1]] => 0
[1,1,1,2] => [1,1,1,2] => [[1,1,1,2]] => 1
[1,1,2,1] => [1,1,1,2] => [[1,1,1,2]] => 1
[1,2,1,1] => [1,1,1,2] => [[1,1,1,2]] => 1
[2,1,1,1] => [1,1,1,2] => [[1,1,1,2]] => 1
[1,1,1,3] => [1,1,1,3] => [[1,1,1,3]] => 2
[1,1,3,1] => [1,1,1,3] => [[1,1,1,3]] => 2
[1,3,1,1] => [1,1,1,3] => [[1,1,1,3]] => 2
[3,1,1,1] => [1,1,1,3] => [[1,1,1,3]] => 2
[1,1,1,4] => [1,1,1,4] => [[1,1,1,4]] => 3
[1,1,4,1] => [1,1,1,4] => [[1,1,1,4]] => 3
[1,4,1,1] => [1,1,1,4] => [[1,1,1,4]] => 3
[4,1,1,1] => [1,1,1,4] => [[1,1,1,4]] => 3
[1,1,2,2] => [1,1,2,2] => [[1,1,2,2]] => 2
[1,2,1,2] => [1,1,2,2] => [[1,1,2,2]] => 2
[1,2,2,1] => [1,1,2,2] => [[1,1,2,2]] => 2
[2,1,1,2] => [1,1,2,2] => [[1,1,2,2]] => 2
[2,1,2,1] => [1,1,2,2] => [[1,1,2,2]] => 2
[2,2,1,1] => [1,1,2,2] => [[1,1,2,2]] => 2
[1,1,2,3] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,1,3,2] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,2,1,3] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,2,3,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,3,1,2] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,3,2,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[2,1,1,3] => [1,1,2,3] => [[1,1,2,3]] => 3
[2,1,3,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[2,3,1,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[3,1,1,2] => [1,1,2,3] => [[1,1,2,3]] => 3
[3,1,2,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[3,2,1,1] => [1,1,2,3] => [[1,1,2,3]] => 3
[1,1,2,4] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,1,4,2] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,2,1,4] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,2,4,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,4,1,2] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,4,2,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[2,1,1,4] => [1,1,2,4] => [[1,1,2,4]] => 4
[2,1,4,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[2,4,1,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[4,1,1,2] => [1,1,2,4] => [[1,1,2,4]] => 4
[4,1,2,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[4,2,1,1] => [1,1,2,4] => [[1,1,2,4]] => 4
[1,1,3,3] => [1,1,3,3] => [[1,1,3,3]] => 4
[1,3,1,3] => [1,1,3,3] => [[1,1,3,3]] => 4
[1,3,3,1] => [1,1,3,3] => [[1,1,3,3]] => 4
[3,1,1,3] => [1,1,3,3] => [[1,1,3,3]] => 4
[3,1,3,1] => [1,1,3,3] => [[1,1,3,3]] => 4
[3,3,1,1] => [1,1,3,3] => [[1,1,3,3]] => 4
[1,1,3,4] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,1,4,3] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,3,1,4] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,3,4,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,4,1,3] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,4,3,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[3,1,1,4] => [1,1,3,4] => [[1,1,3,4]] => 5
[3,1,4,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[3,4,1,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[4,1,1,3] => [1,1,3,4] => [[1,1,3,4]] => 5
[4,1,3,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[4,3,1,1] => [1,1,3,4] => [[1,1,3,4]] => 5
[1,2,2,2] => [1,2,2,2] => [[1,2,2,2]] => 3
[2,1,2,2] => [1,2,2,2] => [[1,2,2,2]] => 3
[2,2,1,2] => [1,2,2,2] => [[1,2,2,2]] => 3
[2,2,2,1] => [1,2,2,2] => [[1,2,2,2]] => 3
[1,2,2,3] => [1,2,2,3] => [[1,2,2,3]] => 4
[1,2,3,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[1,3,2,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,1,2,3] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,1,3,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,2,1,3] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,2,3,1] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,3,1,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[2,3,2,1] => [1,2,2,3] => [[1,2,2,3]] => 4
[3,1,2,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[3,2,1,2] => [1,2,2,3] => [[1,2,2,3]] => 4
[3,2,2,1] => [1,2,2,3] => [[1,2,2,3]] => 4
[1,2,2,4] => [1,2,2,4] => [[1,2,2,4]] => 5
[1,2,4,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[1,4,2,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[2,1,2,4] => [1,2,2,4] => [[1,2,2,4]] => 5
>>> Load all 412 entries. <<<
[2,1,4,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[2,2,1,4] => [1,2,2,4] => [[1,2,2,4]] => 5
[2,2,4,1] => [1,2,2,4] => [[1,2,2,4]] => 5
[2,4,1,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[2,4,2,1] => [1,2,2,4] => [[1,2,2,4]] => 5
[4,1,2,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[4,2,1,2] => [1,2,2,4] => [[1,2,2,4]] => 5
[4,2,2,1] => [1,2,2,4] => [[1,2,2,4]] => 5
[1,2,3,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[1,3,2,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[1,3,3,2] => [1,2,3,3] => [[1,2,3,3]] => 5
[2,1,3,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[2,3,1,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[2,3,3,1] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,1,2,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,1,3,2] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,2,1,3] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,2,3,1] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,3,1,2] => [1,2,3,3] => [[1,2,3,3]] => 5
[3,3,2,1] => [1,2,3,3] => [[1,2,3,3]] => 5
[1,2,3,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,2,4,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,3,2,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,3,4,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,4,2,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,4,3,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,1,3,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,1,4,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,3,1,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,3,4,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,4,1,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[2,4,3,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,1,2,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,1,4,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,2,1,4] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,2,4,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,4,1,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[3,4,2,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,1,2,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,1,3,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,2,1,3] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,2,3,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,3,1,2] => [1,2,3,4] => [[1,2,3,4]] => 6
[4,3,2,1] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,1,1,1,2] => [1,1,1,1,2] => [[1,1,1,1,2]] => 1
[1,1,1,2,1] => [1,1,1,1,2] => [[1,1,1,1,2]] => 1
[1,1,2,1,1] => [1,1,1,1,2] => [[1,1,1,1,2]] => 1
[1,2,1,1,1] => [1,1,1,1,2] => [[1,1,1,1,2]] => 1
[2,1,1,1,1] => [1,1,1,1,2] => [[1,1,1,1,2]] => 1
[1,1,1,1,3] => [1,1,1,1,3] => [[1,1,1,1,3]] => 2
[1,1,1,3,1] => [1,1,1,1,3] => [[1,1,1,1,3]] => 2
[1,1,3,1,1] => [1,1,1,1,3] => [[1,1,1,1,3]] => 2
[1,3,1,1,1] => [1,1,1,1,3] => [[1,1,1,1,3]] => 2
[3,1,1,1,1] => [1,1,1,1,3] => [[1,1,1,1,3]] => 2
[1,1,1,2,2] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,1,2,1,2] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,1,2,2,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,2,1,1,2] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,2,1,2,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,2,2,1,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[2,1,1,1,2] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[2,1,1,2,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[2,1,2,1,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[2,2,1,1,1] => [1,1,1,2,2] => [[1,1,1,2,2]] => 2
[1,1,1,2,3] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,1,3,2] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,2,1,3] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,2,3,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,3,1,2] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,3,2,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,2,1,1,3] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,2,1,3,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,2,3,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,3,1,1,2] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,3,1,2,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,3,2,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[2,1,1,1,3] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[2,1,1,3,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[2,1,3,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[2,3,1,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[3,1,1,1,2] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[3,1,1,2,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[3,1,2,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[3,2,1,1,1] => [1,1,1,2,3] => [[1,1,1,2,3]] => 3
[1,1,1,3,3] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,1,3,1,3] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,1,3,3,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,3,1,1,3] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,3,1,3,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,3,3,1,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[3,1,1,1,3] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[3,1,1,3,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[3,1,3,1,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[3,3,1,1,1] => [1,1,1,3,3] => [[1,1,1,3,3]] => 4
[1,1,2,2,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[1,2,1,2,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[1,2,2,1,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[1,2,2,2,1] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,1,1,2,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,1,2,1,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,1,2,2,1] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,2,1,1,2] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,2,1,2,1] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[2,2,2,1,1] => [1,1,2,2,2] => [[1,1,2,2,2]] => 3
[1,1,2,2,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,1,2,3,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,1,3,2,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,1,2,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,1,3,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,2,1,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,2,3,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,3,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,2,3,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,3,1,2,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,3,2,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,3,2,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,1,2,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,1,3,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,2,1,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,2,3,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,3,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,1,3,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,2,1,1,3] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,2,1,3,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,2,3,1,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,3,1,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,3,1,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[2,3,2,1,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,1,1,2,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,1,2,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,1,2,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,2,1,1,2] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,2,1,2,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[3,2,2,1,1] => [1,1,2,2,3] => [[1,1,2,2,3]] => 4
[1,1,2,3,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,1,3,2,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,1,3,3,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,2,1,3,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,2,3,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,2,3,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,1,2,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,1,3,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,2,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,2,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,3,1,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,3,3,2,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,1,1,3,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,1,3,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,1,3,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,3,1,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,3,1,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[2,3,3,1,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,1,2,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,1,3,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,2,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,2,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,3,1,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,1,3,2,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,2,1,1,3] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,2,1,3,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,2,3,1,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,3,1,1,2] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,3,1,2,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[3,3,2,1,1] => [1,1,2,3,3] => [[1,1,2,3,3]] => 5
[1,1,3,3,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[1,3,1,3,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[1,3,3,1,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[1,3,3,3,1] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,1,1,3,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,1,3,1,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,1,3,3,1] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,3,1,1,3] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,3,1,3,1] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[3,3,3,1,1] => [1,1,3,3,3] => [[1,1,3,3,3]] => 6
[1,2,2,2,2] => [1,2,2,2,2] => [[1,2,2,2,2]] => 4
[2,1,2,2,2] => [1,2,2,2,2] => [[1,2,2,2,2]] => 4
[2,2,1,2,2] => [1,2,2,2,2] => [[1,2,2,2,2]] => 4
[2,2,2,1,2] => [1,2,2,2,2] => [[1,2,2,2,2]] => 4
[2,2,2,2,1] => [1,2,2,2,2] => [[1,2,2,2,2]] => 4
[1,2,2,2,3] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[1,2,2,3,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[1,2,3,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[1,3,2,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,1,2,2,3] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,1,2,3,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,1,3,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,1,2,3] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,1,3,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,2,1,3] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,2,3,1] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,3,1,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,2,3,2,1] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,3,1,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,3,2,1,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[2,3,2,2,1] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[3,1,2,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[3,2,1,2,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[3,2,2,1,2] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[3,2,2,2,1] => [1,2,2,2,3] => [[1,2,2,2,3]] => 5
[1,2,2,3,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,2,3,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,2,3,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,3,2,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,3,2,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,3,3,2,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,1,2,3,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,1,3,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,1,3,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,2,1,3,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,2,3,1,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,2,3,3,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,1,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,1,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,2,1,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,2,3,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,3,1,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[2,3,3,2,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,1,2,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,1,2,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,1,3,2,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,1,2,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,1,3,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,2,1,3] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,2,3,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,3,1,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,2,3,2,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,3,1,2,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,3,2,1,2] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[3,3,2,2,1] => [1,2,2,3,3] => [[1,2,2,3,3]] => 6
[1,2,3,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[1,3,2,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[1,3,3,2,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[1,3,3,3,2] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[2,1,3,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[2,3,1,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[2,3,3,1,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[2,3,3,3,1] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,1,2,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,1,3,2,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,1,3,3,2] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,2,1,3,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,2,3,1,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,2,3,3,1] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,1,2,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,1,3,2] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,2,1,3] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,2,3,1] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,3,1,2] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[3,3,3,2,1] => [1,2,3,3,3] => [[1,2,3,3,3]] => 7
[1,1,1,1,1,2] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[1,1,1,1,2,1] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[1,1,1,2,1,1] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[1,1,2,1,1,1] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[1,2,1,1,1,1] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[2,1,1,1,1,1] => [1,1,1,1,1,2] => [[1,1,1,1,1,2]] => 1
[1,1,1,1,2,2] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,1,2,1,2] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,1,2,2,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,2,1,1,2] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,2,1,2,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,2,2,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,2,1,1,1,2] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,2,1,1,2,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,2,1,2,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,2,2,1,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[2,1,1,1,1,2] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[2,1,1,1,2,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[2,1,1,2,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[2,1,2,1,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[2,2,1,1,1,1] => [1,1,1,1,2,2] => [[1,1,1,1,2,2]] => 2
[1,1,1,2,2,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,1,2,1,2,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,1,2,2,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,1,2,2,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,1,1,2,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,1,2,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,1,2,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,2,1,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,2,1,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,2,2,2,1,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,1,1,2,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,1,2,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,1,2,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,2,1,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,2,1,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,1,2,2,1,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,2,1,1,1,2] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,2,1,1,2,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,2,1,2,1,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[2,2,2,1,1,1] => [1,1,1,2,2,2] => [[1,1,1,2,2,2]] => 3
[1,1,2,2,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[1,2,1,2,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[1,2,2,1,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[1,2,2,2,1,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[1,2,2,2,2,1] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,1,1,2,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,1,2,1,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,1,2,2,1,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,1,2,2,2,1] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,1,1,2,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,1,2,1,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,1,2,2,1] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,2,1,1,2] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,2,1,2,1] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[2,2,2,2,1,1] => [1,1,2,2,2,2] => [[1,1,2,2,2,2]] => 4
[1,2,2,2,2,2] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
[2,1,2,2,2,2] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
[2,2,1,2,2,2] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
[2,2,2,1,2,2] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
[2,2,2,2,1,2] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
[2,2,2,2,2,1] => [1,2,2,2,2,2] => [[1,2,2,2,2,2]] => 5
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Description
The sum of the entries reduced by the index of their row in a semistandard tableau.
This is also the depth of a semistandard tableau $T$ in the crystal $B(\lambda)$ where $\lambda$ is the shape of $T$, independent of the Cartan rank.
Map
insertion tableau
Description
The insertion tableau obtained by applying RSK to the parking function regarded as a word.
Map
to non-decreasing parking function
Description
Return the non-decreasing parking function which underlies the parking function.
Sorts the parking function into an increasing sequence.