Identifier
Values
[1] => [1] => [1,0] => 1
[2] => [2] => [1,0,1,0] => 2
[1,1] => [1,1] => [1,1,0,0] => 2
[3] => [2,1] => [1,0,1,1,0,0] => 3
[2,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 3
[4] => [2,2] => [1,1,1,0,0,0] => 4
[3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 4
[2,2] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 4
[1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 4
[5] => [2,2,1] => [1,1,1,0,0,1,0,0] => 5
[4,1] => [3,2] => [1,0,1,1,1,0,0,0] => 5
[3,2] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 5
[3,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 5
[2,2,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,1,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 5
[6] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
[5,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 6
[4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 6
[4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 6
[3,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 6
[3,2,1] => [3,3] => [1,1,1,0,1,0,0,0] => 6
[3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 6
[2,2,2] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
[2,1,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
[7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 7
[6,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 7
[5,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 7
[5,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 7
[4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 7
[4,2,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 7
[4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[3,3,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 7
[3,2,2] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[3,2,1,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 7
[3,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
[2,2,2,1] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[2,2,1,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[2,1,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[8] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 8
[7,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 8
[6,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 8
[5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 8
[5,2,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 8
[5,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 8
[4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 8
[4,2,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8
[4,2,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[3,3,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 8
[3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[3,2,2,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 8
[3,2,1,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 8
[3,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[2,2,2,2] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[2,2,2,1,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[2,2,1,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 8
[2,1,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[9] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 9
[8,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 9
[7,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
[7,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[6,3] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 9
[6,2,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[6,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 9
[5,4] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 9
[5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[5,2,2] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 9
[5,2,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 9
[5,1,1,1,1] => [2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[4,4,1] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 9
[4,3,2] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[4,3,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[4,2,2,1] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 9
[4,2,1,1,1] => [6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 9
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 9
[3,3,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 9
[3,3,2,1] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 9
[3,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[3,2,2,2] => [8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[3,2,2,1,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 9
[3,2,1,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[2,2,2,2,1] => [9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[2,2,2,1,1,1] => [7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[2,2,1,1,1,1,1] => [5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 9
[2,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[10] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 10
[9,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 10
[8,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[8,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 10
[7,3] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
>>> Load all 294 entries. <<<
[7,2,1] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 10
[7,1,1,1] => [2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 10
[6,4] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 10
[6,3,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 10
[6,2,2] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[6,2,1,1] => [6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 10
[6,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[5,5] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[5,4,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 10
[5,3,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10
[5,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[5,2,2,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10
[5,2,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 10
[5,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[4,4,2] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 10
[4,4,1,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10
[4,3,3] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10
[4,3,2,1] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 10
[4,3,1,1,1] => [5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 10
[4,2,2,2] => [8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[4,2,2,1,1] => [8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[4,2,1,1,1,1] => [6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[3,3,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[3,3,2,2] => [7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10
[3,3,2,1,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 10
[3,3,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[3,2,2,2,1] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 10
[3,2,2,1,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10
[3,2,1,1,1,1,1] => [3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[3,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[2,2,2,2,2] => [10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[2,2,2,2,1,1] => [9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[2,2,2,1,1,1,1] => [7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10
[2,2,1,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10
[2,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[11] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11
[10,1] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[9,2] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[9,1,1] => [2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 11
[8,3] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[8,2,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 11
[7,4] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[7,3,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[7,2,1,1] => [4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 11
[6,5] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 11
[6,4,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11
[6,3,2] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 11
[6,3,1,1] => [5,2,2,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 11
[5,5,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 11
[5,4,2] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 11
[5,4,1,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[5,3,3] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[5,3,2,1] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 11
[5,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[4,4,3] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 11
[4,4,2,1] => [7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11
[4,3,3,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 11
[4,3,2,1,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[3,3,3,2] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[3,3,2,2,1] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[3,3,2,1,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
[3,2,2,2,2] => [10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 11
[3,2,2,1,1,1,1] => [5,3,1,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 11
[3,2,1,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[2,2,2,2,1,1,1] => [9,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 11
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11
[12] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[11,1] => [2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 12
[10,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[9,3] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[9,2,1] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 12
[8,4] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 12
[8,3,1] => [4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 12
[7,5] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[7,4,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 12
[7,3,2] => [5,2,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[7,2,2,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[6,6] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 12
[6,5,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
[6,4,2] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 12
[6,4,1,1] => [6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 12
[6,3,3] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 12
[6,3,2,1] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[5,4,2,1] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 12
[5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 12
[5,3,3,1] => [3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[5,3,2,1,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[4,4,4] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[4,4,3,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 12
[4,3,3,1,1] => [5,3,2,1,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 12
[4,3,2,2,1] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 12
[3,3,3,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 12
[3,3,3,2,1] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 12
[3,3,2,2,1,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[3,3,2,1,1,1,1] => [3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 12
[13] => [2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 13
[12,1] => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[10,3] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 13
[9,4] => [4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 13
[8,5] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 13
[8,4,1] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[7,6] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 13
[7,4,1,1] => [4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 13
[7,3,3] => [3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[7,3,2,1] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 13
[6,6,1] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[6,5,2] => [6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[6,4,3] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 13
[6,3,3,1] => [5,4,2,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 13
[5,5,3] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 13
[5,5,2,1] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 13
[5,4,4] => [6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 13
[5,4,3,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[5,3,3,2] => [5,3,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 13
[5,3,2,2,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[4,4,4,1] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[4,3,3,2,1] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 13
[3,3,3,2,1,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 13
[3,3,2,2,1,1,1] => [5,3,3,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 13
[14] => [2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 14
[11,2,1] => [3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[10,4] => [4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[9,4,1] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
[8,6] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[8,3,3] => [5,4,2,2,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[8,3,2,1] => [5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 14
[7,7] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[7,6,1] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 14
[7,4,3] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 14
[6,6,2] => [6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[6,5,3] => [5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
[6,5,2,1] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 14
[6,4,4] => [6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 14
[5,5,2,1,1] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 14
[5,4,4,1] => [6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 14
[5,3,3,2,1] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 14
[4,4,3,3] => [7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[4,4,3,2,1] => [7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[4,3,2,1,1,1,1,1] => [5,5,1,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 14
[3,3,3,3,2] => [5,3,3,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[3,3,3,2,2,1] => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 14
[3,3,3,2,1,1,1] => [3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 14
[14,1] => [3,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[10,5] => [4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 15
[9,6] => [4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 15
[9,3,2,1] => [3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 15
[8,7] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 15
[8,6,1] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 15
[7,6,1,1] => [4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 15
[7,5,2,1] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 15
[6,6,3] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 15
[6,5,4] => [6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 15
[6,3,3,2,1] => [5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[5,5,5] => [5,4,3,2,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 15
[5,5,4,1] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 15
[5,4,3,3] => [5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[5,4,3,2,1] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 15
[4,4,4,3] => [8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[4,4,3,2,1,1] => [7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 15
[3,3,3,3,3] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 15
[3,3,3,3,2,1] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[16] => [2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[11,4,1] => [4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 16
[10,6] => [4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 16
[9,6,1] => [4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 16
[8,8] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 16
[8,7,1] => [4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 16
[8,5,2,1] => [5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 16
[7,6,3] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 16
[7,3,3,2,1] => [3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 16
[6,6,4] => [6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[6,5,4,1] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 16
[5,5,3,2,1] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 16
[5,4,3,2,1,1] => [5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 16
[4,4,4,4] => [8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[4,3,3,3,2,1] => [5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 16
[3,3,3,3,2,1,1] => [3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 16
[16,1] => [3,2,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[11,3,2,1] => [3,3,3,2,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[10,7] => [4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 17
[9,8] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 17
[8,8,1] => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 17
[7,7,2,1] => [4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 17
[7,4,3,2,1] => [5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 17
[6,6,5] => [6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 17
[5,5,4,3] => [5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 17
[5,4,4,4] => [8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 17
[5,3,3,3,2,1] => [3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 17
[4,4,4,4,1] => [9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
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
Description
The area of the parallelogram polyomino associated with the Dyck path.
The (bivariate) generating function is given in [1].
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.