Identifier
Values
[1] => [1] => 0
[2] => [1,1] => 1
[1,1] => [2] => 0
[3] => [1,1,1] => 1
[2,1] => [2,1] => 0
[1,1,1] => [3] => 0
[4] => [1,1,1,1] => 1
[3,1] => [2,1,1] => 1
[2,2] => [2,2] => 1
[2,1,1] => [3,1] => 0
[1,1,1,1] => [4] => 0
[5] => [1,1,1,1,1] => 1
[4,1] => [2,1,1,1] => 1
[3,2] => [2,2,1] => 1
[3,1,1] => [3,1,1] => 1
[2,2,1] => [3,2] => 0
[2,1,1,1] => [4,1] => 0
[1,1,1,1,1] => [5] => 0
[6] => [1,1,1,1,1,1] => 1
[5,1] => [2,1,1,1,1] => 1
[4,2] => [2,2,1,1] => 2
[4,1,1] => [3,1,1,1] => 1
[3,3] => [2,2,2] => 1
[3,2,1] => [3,2,1] => 0
[3,1,1,1] => [4,1,1] => 1
[2,2,2] => [3,3] => 1
[2,2,1,1] => [4,2] => 0
[2,1,1,1,1] => [5,1] => 0
[1,1,1,1,1,1] => [6] => 0
[7] => [1,1,1,1,1,1,1] => 1
[6,1] => [2,1,1,1,1,1] => 1
[5,2] => [2,2,1,1,1] => 2
[5,1,1] => [3,1,1,1,1] => 1
[4,3] => [2,2,2,1] => 1
[4,2,1] => [3,2,1,1] => 1
[4,1,1,1] => [4,1,1,1] => 1
[3,3,1] => [3,2,2] => 1
[3,2,2] => [3,3,1] => 1
[3,2,1,1] => [4,2,1] => 0
[3,1,1,1,1] => [5,1,1] => 1
[2,2,2,1] => [4,3] => 0
[2,2,1,1,1] => [5,2] => 0
[2,1,1,1,1,1] => [6,1] => 0
[1,1,1,1,1,1,1] => [7] => 0
[8] => [1,1,1,1,1,1,1,1] => 1
[7,1] => [2,1,1,1,1,1,1] => 1
[6,2] => [2,2,1,1,1,1] => 2
[6,1,1] => [3,1,1,1,1,1] => 1
[5,3] => [2,2,2,1,1] => 2
[5,2,1] => [3,2,1,1,1] => 1
[5,1,1,1] => [4,1,1,1,1] => 1
[4,4] => [2,2,2,2] => 1
[4,3,1] => [3,2,2,1] => 1
[4,2,2] => [3,3,1,1] => 2
[4,2,1,1] => [4,2,1,1] => 1
[4,1,1,1,1] => [5,1,1,1] => 1
[3,3,2] => [3,3,2] => 1
[3,3,1,1] => [4,2,2] => 1
[3,2,2,1] => [4,3,1] => 0
[3,2,1,1,1] => [5,2,1] => 0
[3,1,1,1,1,1] => [6,1,1] => 1
[2,2,2,2] => [4,4] => 1
[2,2,2,1,1] => [5,3] => 0
[2,2,1,1,1,1] => [6,2] => 0
[2,1,1,1,1,1,1] => [7,1] => 0
[1,1,1,1,1,1,1,1] => [8] => 0
[9] => [1,1,1,1,1,1,1,1,1] => 1
[8,1] => [2,1,1,1,1,1,1,1] => 1
[7,2] => [2,2,1,1,1,1,1] => 2
[7,1,1] => [3,1,1,1,1,1,1] => 1
[6,3] => [2,2,2,1,1,1] => 2
[6,2,1] => [3,2,1,1,1,1] => 1
[6,1,1,1] => [4,1,1,1,1,1] => 1
[5,4] => [2,2,2,2,1] => 1
[5,3,1] => [3,2,2,1,1] => 2
[5,2,2] => [3,3,1,1,1] => 2
[5,2,1,1] => [4,2,1,1,1] => 1
[5,1,1,1,1] => [5,1,1,1,1] => 1
[4,4,1] => [3,2,2,2] => 1
[4,3,2] => [3,3,2,1] => 1
[4,3,1,1] => [4,2,2,1] => 1
[4,2,2,1] => [4,3,1,1] => 1
[4,2,1,1,1] => [5,2,1,1] => 1
[4,1,1,1,1,1] => [6,1,1,1] => 1
[3,3,3] => [3,3,3] => 1
[3,3,2,1] => [4,3,2] => 0
[3,3,1,1,1] => [5,2,2] => 1
[3,2,2,2] => [4,4,1] => 1
[3,2,2,1,1] => [5,3,1] => 0
[3,2,1,1,1,1] => [6,2,1] => 0
[3,1,1,1,1,1,1] => [7,1,1] => 1
[2,2,2,2,1] => [5,4] => 0
[2,2,2,1,1,1] => [6,3] => 0
[2,2,1,1,1,1,1] => [7,2] => 0
[2,1,1,1,1,1,1,1] => [8,1] => 0
[1,1,1,1,1,1,1,1,1] => [9] => 0
[10] => [1,1,1,1,1,1,1,1,1,1] => 1
[9,1] => [2,1,1,1,1,1,1,1,1] => 1
[8,2] => [2,2,1,1,1,1,1,1] => 2
[8,1,1] => [3,1,1,1,1,1,1,1] => 1
[7,3] => [2,2,2,1,1,1,1] => 2
>>> Load all 529 entries. <<<
[7,2,1] => [3,2,1,1,1,1,1] => 1
[7,1,1,1] => [4,1,1,1,1,1,1] => 1
[6,4] => [2,2,2,2,1,1] => 2
[6,3,1] => [3,2,2,1,1,1] => 2
[6,2,2] => [3,3,1,1,1,1] => 2
[6,2,1,1] => [4,2,1,1,1,1] => 1
[6,1,1,1,1] => [5,1,1,1,1,1] => 1
[5,5] => [2,2,2,2,2] => 1
[5,4,1] => [3,2,2,2,1] => 1
[5,3,2] => [3,3,2,1,1] => 2
[5,3,1,1] => [4,2,2,1,1] => 2
[5,2,2,1] => [4,3,1,1,1] => 1
[5,2,1,1,1] => [5,2,1,1,1] => 1
[5,1,1,1,1,1] => [6,1,1,1,1] => 1
[4,4,2] => [3,3,2,2] => 2
[4,4,1,1] => [4,2,2,2] => 1
[4,3,3] => [3,3,3,1] => 1
[4,3,2,1] => [4,3,2,1] => 0
[4,3,1,1,1] => [5,2,2,1] => 1
[4,2,2,2] => [4,4,1,1] => 2
[4,2,2,1,1] => [5,3,1,1] => 1
[4,2,1,1,1,1] => [6,2,1,1] => 1
[4,1,1,1,1,1,1] => [7,1,1,1] => 1
[3,3,3,1] => [4,3,3] => 1
[3,3,2,2] => [4,4,2] => 1
[3,3,2,1,1] => [5,3,2] => 0
[3,3,1,1,1,1] => [6,2,2] => 1
[3,2,2,2,1] => [5,4,1] => 0
[3,2,2,1,1,1] => [6,3,1] => 0
[3,2,1,1,1,1,1] => [7,2,1] => 0
[3,1,1,1,1,1,1,1] => [8,1,1] => 1
[2,2,2,2,2] => [5,5] => 1
[2,2,2,2,1,1] => [6,4] => 0
[2,2,2,1,1,1,1] => [7,3] => 0
[2,2,1,1,1,1,1,1] => [8,2] => 0
[2,1,1,1,1,1,1,1,1] => [9,1] => 0
[1,1,1,1,1,1,1,1,1,1] => [10] => 0
[11] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[10,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[9,2] => [2,2,1,1,1,1,1,1,1] => 2
[9,1,1] => [3,1,1,1,1,1,1,1,1] => 1
[8,3] => [2,2,2,1,1,1,1,1] => 2
[8,2,1] => [3,2,1,1,1,1,1,1] => 1
[8,1,1,1] => [4,1,1,1,1,1,1,1] => 1
[7,4] => [2,2,2,2,1,1,1] => 2
[7,3,1] => [3,2,2,1,1,1,1] => 2
[7,2,2] => [3,3,1,1,1,1,1] => 2
[7,1,1,1,1] => [5,1,1,1,1,1,1] => 1
[6,5] => [2,2,2,2,2,1] => 1
[6,4,1] => [3,2,2,2,1,1] => 2
[6,2,2,1] => [4,3,1,1,1,1] => 1
[6,2,1,1,1] => [5,2,1,1,1,1] => 1
[6,1,1,1,1,1] => [6,1,1,1,1,1] => 1
[5,5,1] => [3,2,2,2,2] => 1
[5,4,2] => [3,3,2,2,1] => 2
[5,4,1,1] => [4,2,2,2,1] => 1
[5,3,3] => [3,3,3,1,1] => 2
[5,3,2,1] => [4,3,2,1,1] => 1
[5,3,1,1,1] => [5,2,2,1,1] => 2
[5,2,2,2] => [4,4,1,1,1] => 2
[5,2,2,1,1] => [5,3,1,1,1] => 1
[5,1,1,1,1,1,1] => [7,1,1,1,1] => 1
[4,4,3] => [3,3,3,2] => 1
[4,4,2,1] => [4,3,2,2] => 1
[4,4,1,1,1] => [5,2,2,2] => 1
[4,3,3,1] => [4,3,3,1] => 1
[4,3,2,2] => [4,4,2,1] => 1
[4,3,2,1,1] => [5,3,2,1] => 0
[4,3,1,1,1,1] => [6,2,2,1] => 1
[4,2,2,2,1] => [5,4,1,1] => 1
[4,2,2,1,1,1] => [6,3,1,1] => 1
[4,1,1,1,1,1,1,1] => [8,1,1,1] => 1
[3,3,3,2] => [4,4,3] => 1
[3,3,3,1,1] => [5,3,3] => 1
[3,3,2,2,1] => [5,4,2] => 0
[3,3,2,1,1,1] => [6,3,2] => 0
[3,3,1,1,1,1,1] => [7,2,2] => 1
[3,2,2,2,2] => [5,5,1] => 1
[3,2,2,2,1,1] => [6,4,1] => 0
[3,2,1,1,1,1,1,1] => [8,2,1] => 0
[3,1,1,1,1,1,1,1,1] => [9,1,1] => 1
[2,2,2,2,2,1] => [6,5] => 0
[2,2,2,2,1,1,1] => [7,4] => 0
[2,2,2,1,1,1,1,1] => [8,3] => 0
[2,1,1,1,1,1,1,1,1,1] => [10,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[12] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[10,2] => [2,2,1,1,1,1,1,1,1,1] => 2
[8,4] => [2,2,2,2,1,1,1,1] => 2
[8,3,1] => [3,2,2,1,1,1,1,1] => 2
[8,2,2] => [3,3,1,1,1,1,1,1] => 2
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => 1
[7,5] => [2,2,2,2,2,1,1] => 2
[7,2,2,1] => [4,3,1,1,1,1,1] => 1
[7,2,1,1,1] => [5,2,1,1,1,1,1] => 1
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => 1
[6,6] => [2,2,2,2,2,2] => 1
[6,5,1] => [3,2,2,2,2,1] => 1
[6,4,2] => [3,3,2,2,1,1] => 3
[6,3,1,1,1] => [5,2,2,1,1,1] => 2
[6,2,2,1,1] => [5,3,1,1,1,1] => 1
[6,2,1,1,1,1] => [6,2,1,1,1,1] => 1
[5,5,2] => [3,3,2,2,2] => 2
[5,4,3] => [3,3,3,2,1] => 1
[5,4,2,1] => [4,3,2,2,1] => 1
[5,4,1,1,1] => [5,2,2,2,1] => 1
[5,3,3,1] => [4,3,3,1,1] => 2
[5,3,2,2] => [4,4,2,1,1] => 2
[5,3,2,1,1] => [5,3,2,1,1] => 1
[5,3,1,1,1,1] => [6,2,2,1,1] => 2
[5,2,2,2,1] => [5,4,1,1,1] => 1
[5,2,2,1,1,1] => [6,3,1,1,1] => 1
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 1
[4,4,4] => [3,3,3,3] => 1
[4,4,3,1] => [4,3,3,2] => 1
[4,4,2,2] => [4,4,2,2] => 2
[4,4,2,1,1] => [5,3,2,2] => 1
[4,4,1,1,1,1] => [6,2,2,2] => 1
[4,3,3,2] => [4,4,3,1] => 1
[4,3,3,1,1] => [5,3,3,1] => 1
[4,3,2,2,1] => [5,4,2,1] => 0
[4,2,2,2,2] => [5,5,1,1] => 2
[4,2,2,2,1,1] => [6,4,1,1] => 1
[4,2,1,1,1,1,1,1] => [8,2,1,1] => 1
[3,3,3,3] => [4,4,4] => 1
[3,3,3,2,1] => [5,4,3] => 0
[3,3,3,1,1,1] => [6,3,3] => 1
[3,3,2,2,2] => [5,5,2] => 1
[3,3,2,2,1,1] => [6,4,2] => 0
[3,3,1,1,1,1,1,1] => [8,2,2] => 1
[3,2,2,2,2,1] => [6,5,1] => 0
[3,2,2,2,1,1,1] => [7,4,1] => 0
[3,2,2,1,1,1,1,1] => [8,3,1] => 0
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => 1
[2,2,2,2,2,2] => [6,6] => 1
[2,2,2,2,2,1,1] => [7,5] => 0
[2,2,2,2,1,1,1,1] => [8,4] => 0
[2,2,2,1,1,1,1,1,1] => [9,3] => 0
[2,2,1,1,1,1,1,1,1,1] => [10,2] => 0
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 0
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => 1
[9,4] => [2,2,2,2,1,1,1,1,1] => 2
[8,3,2] => [3,3,2,1,1,1,1,1] => 2
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => 1
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => 1
[7,6] => [2,2,2,2,2,2,1] => 1
[7,5,1] => [3,2,2,2,2,1,1] => 2
[7,3,1,1,1] => [5,2,2,1,1,1,1] => 2
[7,2,2,1,1] => [5,3,1,1,1,1,1] => 1
[6,6,1] => [3,2,2,2,2,2] => 1
[6,5,2] => [3,3,2,2,2,1] => 2
[6,4,1,1,1] => [5,2,2,2,1,1] => 2
[6,3,2,1,1] => [5,3,2,1,1,1] => 1
[6,3,1,1,1,1] => [6,2,2,1,1,1] => 2
[6,2,2,2,1] => [5,4,1,1,1,1] => 1
[6,2,2,1,1,1] => [6,3,1,1,1,1] => 1
[5,5,3] => [3,3,3,2,2] => 2
[5,4,4] => [3,3,3,3,1] => 1
[5,4,3,1] => [4,3,3,2,1] => 1
[5,4,2,2] => [4,4,2,2,1] => 2
[5,4,2,1,1] => [5,3,2,2,1] => 1
[5,3,3,2] => [4,4,3,1,1] => 2
[5,3,3,1,1] => [5,3,3,1,1] => 2
[5,3,2,2,1] => [5,4,2,1,1] => 1
[4,4,4,1] => [4,3,3,3] => 1
[4,4,3,2] => [4,4,3,2] => 1
[4,4,3,1,1] => [5,3,3,2] => 1
[4,4,2,2,1] => [5,4,2,2] => 1
[4,4,2,1,1,1] => [6,3,2,2] => 1
[4,3,3,3] => [4,4,4,1] => 1
[4,3,3,2,1] => [5,4,3,1] => 0
[4,3,2,2,1,1] => [6,4,2,1] => 0
[4,2,2,2,2,1] => [6,5,1,1] => 1
[4,2,2,1,1,1,1,1] => [8,3,1,1] => 1
[3,3,3,3,1] => [5,4,4] => 1
[3,3,3,2,2] => [5,5,3] => 1
[3,3,3,2,1,1] => [6,4,3] => 0
[3,3,3,1,1,1,1] => [7,3,3] => 1
[3,3,2,2,2,1] => [6,5,2] => 0
[3,3,2,2,1,1,1] => [7,4,2] => 0
[3,3,2,1,1,1,1,1] => [8,3,2] => 0
[3,3,1,1,1,1,1,1,1] => [9,2,2] => 1
[3,2,2,2,2,2] => [6,6,1] => 1
[3,2,2,2,2,1,1] => [7,5,1] => 0
[3,2,2,2,1,1,1,1] => [8,4,1] => 0
[2,2,2,2,2,2,1] => [7,6] => 0
[2,2,2,2,2,1,1,1] => [8,5] => 0
[2,2,2,1,1,1,1,1,1,1] => [10,3] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[10,2,2] => [3,3,1,1,1,1,1,1,1,1] => 2
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => 1
[8,5,1] => [3,2,2,2,2,1,1,1] => 2
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => 2
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => 1
[7,7] => [2,2,2,2,2,2,2] => 1
[7,3,2,1,1] => [5,3,2,1,1,1,1] => 1
[7,2,2,2,1] => [5,4,1,1,1,1,1] => 1
[6,6,2] => [3,3,2,2,2,2] => 2
[6,5,3] => [3,3,3,2,2,1] => 2
[6,5,2,1] => [4,3,2,2,2,1] => 1
[6,5,1,1,1] => [5,2,2,2,2,1] => 1
[6,4,4] => [3,3,3,3,1,1] => 2
[6,4,2,1,1] => [5,3,2,2,1,1] => 2
[6,3,2,2,1] => [5,4,2,1,1,1] => 1
[6,2,2,2,2] => [5,5,1,1,1,1] => 2
[5,5,4] => [3,3,3,3,2] => 1
[5,5,2,1,1] => [5,3,2,2,2] => 1
[5,5,1,1,1,1] => [6,2,2,2,2] => 1
[5,4,3,2] => [4,4,3,2,1] => 1
[5,4,3,1,1] => [5,3,3,2,1] => 1
[5,4,2,2,1] => [5,4,2,2,1] => 1
[5,3,3,3] => [4,4,4,1,1] => 2
[5,3,3,2,1] => [5,4,3,1,1] => 1
[5,2,2,2,2,1] => [6,5,1,1,1] => 1
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => 1
[4,4,4,2] => [4,4,3,3] => 2
[4,4,4,1,1] => [5,3,3,3] => 1
[4,4,3,3] => [4,4,4,2] => 1
[4,4,3,2,1] => [5,4,3,2] => 0
[4,4,2,2,1,1] => [6,4,2,2] => 1
[4,2,2,2,2,2] => [6,6,1,1] => 2
[3,3,3,3,2] => [5,5,4] => 1
[3,3,3,3,1,1] => [6,4,4] => 1
[3,3,3,2,2,1] => [6,5,3] => 0
[3,3,3,2,1,1,1] => [7,4,3] => 0
[3,3,2,2,2,2] => [6,6,2] => 1
[3,3,2,2,2,1,1] => [7,5,2] => 0
[3,3,2,2,1,1,1,1] => [8,4,2] => 0
[3,2,2,2,2,1,1,1] => [8,5,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 1
[2,2,2,2,2,2,2] => [7,7] => 1
[2,2,2,2,2,2,1,1] => [8,6] => 0
[2,2,2,2,2,1,1,1,1] => [9,5] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1] => 1
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => 1
[7,4,2,1,1] => [5,3,2,2,1,1,1] => 2
[6,6,3] => [3,3,3,2,2,2] => 2
[6,5,4] => [3,3,3,3,2,1] => 1
[6,5,2,1,1] => [5,3,2,2,2,1] => 1
[6,5,1,1,1,1] => [6,2,2,2,2,1] => 1
[6,3,3,3] => [4,4,4,1,1,1] => 2
[6,3,3,2,1] => [5,4,3,1,1,1] => 1
[6,2,2,2,2,1] => [6,5,1,1,1,1] => 1
[5,5,5] => [3,3,3,3,3] => 1
[5,5,4,1] => [4,3,3,3,2] => 1
[5,4,3,2,1] => [5,4,3,2,1] => 0
[5,3,3,2,1,1] => [6,4,3,1,1] => 1
[4,4,4,3] => [4,4,4,3] => 1
[4,4,4,2,1] => [5,4,3,3] => 1
[4,4,4,1,1,1] => [6,3,3,3] => 1
[3,3,3,3,3] => [5,5,5] => 1
[3,3,3,3,2,1] => [6,5,4] => 0
[3,3,3,2,2,2] => [6,6,3] => 1
[3,3,3,2,2,1,1] => [7,5,3] => 0
[3,3,2,2,2,1,1,1] => [8,5,2] => 0
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => 1
[3,2,2,2,2,1,1,1,1] => [9,5,1] => 0
[2,2,2,2,2,2,2,1] => [8,7] => 0
[2,2,2,2,2,2,1,1,1] => [9,6] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1] => 2
[10,6] => [2,2,2,2,2,2,1,1,1,1] => 2
[8,8] => [2,2,2,2,2,2,2,2] => 1
[8,4,4] => [3,3,3,3,1,1,1,1] => 2
[7,7,2] => [3,3,2,2,2,2,2] => 2
[6,6,4] => [3,3,3,3,2,2] => 2
[6,5,4,1] => [4,3,3,3,2,1] => 1
[6,5,2,2,1] => [5,4,2,2,2,1] => 1
[6,4,3,2,1] => [5,4,3,2,1,1] => 1
[5,5,5,1] => [4,3,3,3,3] => 1
[5,5,4,2] => [4,4,3,3,2] => 2
[5,5,3,3] => [4,4,4,2,2] => 2
[5,5,2,2,2] => [5,5,2,2,2] => 2
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 1
[4,4,4,4] => [4,4,4,4] => 1
[4,4,4,3,1] => [5,4,4,3] => 1
[4,4,4,2,2] => [5,5,3,3] => 2
[4,4,4,2,1,1] => [6,4,3,3] => 1
[4,4,2,2,2,2] => [6,6,2,2] => 2
[4,3,3,2,2,1,1] => [7,5,3,1] => 0
[3,3,3,3,3,1] => [6,5,5] => 1
[3,3,3,3,2,2] => [6,6,4] => 1
[3,3,3,2,2,2,1] => [7,6,3] => 0
[3,3,3,2,2,1,1,1] => [8,5,3] => 0
[3,3,2,2,2,2,1,1] => [8,6,2] => 0
[2,2,2,2,2,2,2,2] => [8,8] => 1
[2,2,2,2,2,2,1,1,1,1] => [10,6] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[8,8,1] => [3,2,2,2,2,2,2,2] => 1
[6,6,5] => [3,3,3,3,3,2] => 1
[6,5,4,1,1] => [5,3,3,3,2,1] => 1
[6,5,3,3] => [4,4,4,2,2,1] => 2
[6,5,3,2,1] => [5,4,3,2,2,1] => 1
[6,5,2,2,2] => [5,5,2,2,2,1] => 2
[6,4,4,3] => [4,4,4,3,1,1] => 2
[6,4,4,1,1,1] => [6,3,3,3,1,1] => 2
[6,3,3,3,2] => [5,5,4,1,1,1] => 2
[6,3,3,3,1,1] => [6,4,4,1,1,1] => 2
[5,5,5,2] => [4,4,3,3,3] => 2
[5,5,4,3] => [4,4,4,3,2] => 1
[5,5,4,1,1,1] => [6,3,3,3,2] => 1
[5,5,2,2,2,1] => [6,5,2,2,2] => 1
[4,4,4,4,1] => [5,4,4,4] => 1
[4,4,4,3,2] => [5,5,4,3] => 1
[4,4,4,3,1,1] => [6,4,4,3] => 1
[4,4,4,2,2,1] => [6,5,3,3] => 1
[4,4,3,2,2,1,1] => [7,5,3,2] => 0
[3,3,3,2,2,2,1,1] => [8,6,3] => 0
[3,2,2,2,2,2,2,2] => [8,8,1] => 1
[2,2,2,2,2,2,2,2,1] => [9,8] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 0
[] => [] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[5,5,4,3,2,1] => [6,5,4,3,2] => 0
[6,4,4,3,2,1] => [6,5,4,3,1,1] => 1
[5,4,4,3,2,1] => [6,5,4,3,1] => 0
[4,4,4,3,2,1] => [6,5,4,3] => 0
[6,5,3,3,2,1] => [6,5,4,2,2,1] => 1
[5,5,3,3,2,1] => [6,5,4,2,2] => 1
[6,3,3,3,2,1] => [6,5,4,1,1,1] => 1
[6,5,4,2,2,1] => [6,5,3,3,2,1] => 1
[5,5,4,2,2,1] => [6,5,3,3,2] => 1
[6,4,4,2,2,1] => [6,5,3,3,1,1] => 2
[6,5,2,2,2,1] => [6,5,2,2,2,1] => 1
[6,5,4,3,1,1] => [6,4,4,3,2,1] => 1
[5,5,4,3,1,1] => [6,4,4,3,2] => 1
[6,4,4,3,1,1] => [6,4,4,3,1,1] => 2
[6,5,3,3,1,1] => [6,4,4,2,2,1] => 2
[5,5,3,3,1,1] => [6,4,4,2,2] => 2
[6,5,4,1,1,1] => [6,3,3,3,2,1] => 1
[6,5,4,3,2] => [5,5,4,3,2,1] => 1
[5,5,4,3,2] => [5,5,4,3,2] => 1
[6,4,4,3,2] => [5,5,4,3,1,1] => 2
[6,5,3,3,2] => [5,5,4,2,2,1] => 2
[5,5,3,3,2] => [5,5,4,2,2] => 2
[6,5,4,2,2] => [5,5,3,3,2,1] => 2
[5,5,4,2,2] => [5,5,3,3,2] => 2
[6,4,4,2,2] => [5,5,3,3,1,1] => 3
[6,5,4,3,1] => [5,4,4,3,2,1] => 1
[6,5,4,2,1] => [5,4,3,3,2,1] => 1
[6,5,4,3] => [4,4,4,3,2,1] => 1
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[6,6,5,4,3,2,1] => [7,6,5,4,3,2] => 0
[6,6,2,2,2,2,1] => [7,6,2,2,2,2] => 1
[7,6,5,4,3,2] => [6,6,5,4,3,2,1] => 1
[4,4,4,4,3,2] => [6,6,5,4] => 1
[6,6,2,2,2,2] => [6,6,2,2,2,2] => 2
[7,6,5,4,3,1] => [6,5,5,4,3,2,1] => 1
[7,6,5,4,2,1] => [6,5,4,4,3,2,1] => 1
[7,6,5,3,2,1] => [6,5,4,3,3,2,1] => 1
[7,6,4,3,2,1] => [6,5,4,3,2,2,1] => 1
[7,5,4,3,2,1] => [6,5,4,3,2,1,1] => 1
[7,4,4,3,2,1] => [6,5,4,3,1,1,1] => 1
[7,6,3,3,2,1] => [6,5,4,2,2,2,1] => 1
[7,3,3,3,2,1] => [6,5,4,1,1,1,1] => 1
[7,6,5,2,2,1] => [6,5,3,3,3,2,1] => 1
[7,6,2,2,2,1] => [6,5,2,2,2,2,1] => 1
[7,6,5,4,1,1] => [6,4,4,4,3,2,1] => 1
[4,4,4,4,1,1] => [6,4,4,4] => 1
[7,6,5,1,1,1] => [6,3,3,3,3,2,1] => 1
[7,6,5,4,3] => [5,5,5,4,3,2,1] => 1
[4,4,4,4,2] => [5,5,4,4] => 2
[7,6,5,4,1] => [5,4,4,4,3,2,1] => 1
[7,6,5,4] => [4,4,4,4,3,2,1] => 1
[5,5,5,4] => [4,4,4,4,3] => 1
[5,5,4,4] => [4,4,4,4,2] => 1
[2,2,2,2,2,2,2,2,2] => [9,9] => 1
[3,3,3,3,3,3] => [6,6,6] => 1
[3,3,3,3,3,3,3,3] => [8,8,8] => 1
[3,3,3,3,3,3,1] => [7,6,6] => 1
[4,4,4,4,4] => [5,5,5,5] => 1
[4,4,4,4,4,4] => [6,6,6,6] => 1
[5,5,5,5] => [4,4,4,4,4] => 1
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16] => 1
[6,6,6,6] => [4,4,4,4,4,4] => 1
[6,2,2,2,2,2,2] => [7,7,1,1,1,1] => 2
[6,6,6] => [3,3,3,3,3,3] => 1
[10,4,4] => [3,3,3,3,1,1,1,1,1,1] => 2
[10,10] => [2,2,2,2,2,2,2,2,2,2] => 1
[6,6,6,6,6] => [5,5,5,5,5,5] => 1
[6,6,6,4,3,3] => [6,6,6,4,3,3] => 2
[10,10,10,10] => [4,4,4,4,4,4,4,4,4,4] => 1
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [24,24,24,24,24] => 1
[5,5,5,5,5,5,5,5,5,5,5,5] => [12,12,12,12,12] => 1
[15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 1
[5,5,5,5,5,5] => [6,6,6,6,6] => 1
[15,5,5] => [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 2
[6,6,6,2] => [4,4,3,3,3,3] => 2
[7,7,7] => [3,3,3,3,3,3,3] => 1
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0
[9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1] => 1
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1] => 1
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1] => 1
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => 1
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => 1
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => 1
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => 1
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1] => 1
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1] => 1
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => 1
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => 1
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => 1
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => 1
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => 1
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1] => 1
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15] => 1
[5,5,5,5,5] => [5,5,5,5,5] => 1
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => 1
[3,3,3,3,3,3,1,1] => [8,6,6] => 1
[6,6,6,1] => [4,3,3,3,3,3] => 1
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => 0
[4,4,3,3,2,2,1,1] => [8,6,4,2] => 0
[5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2] => 0
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Description
The number of distinct parts of a partition that occur at least twice.
See Section 3.3.1 of [2].
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.