Identifier
Values
[2] => [1,0,1,0] => [1,1] => 3
[1,1] => [1,1,0,0] => [2] => 3
[3] => [1,0,1,0,1,0] => [1,1,1] => 4
[2,1] => [1,0,1,1,0,0] => [1,2] => 4
[1,1,1] => [1,1,0,1,0,0] => [3] => 4
[4] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => 5
[3,1] => [1,0,1,0,1,1,0,0] => [1,1,2] => 5
[2,2] => [1,1,1,0,0,0] => [3] => 4
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,3] => 5
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [4] => 5
[5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 6
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 6
[3,2] => [1,0,1,1,1,0,0,0] => [1,3] => 5
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => 6
[2,2,1] => [1,1,1,0,0,1,0,0] => [4] => 5
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,4] => 6
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [5] => 6
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 7
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 7
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 6
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => 7
[3,3] => [1,1,1,0,1,0,0,0] => [4] => 5
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4] => 6
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => 7
[2,2,2] => [1,1,1,1,0,0,0,0] => [4] => 5
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [5] => 6
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => 7
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [6] => 7
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 8
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 8
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 7
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => 8
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4] => 6
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => 7
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => 8
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [5] => 6
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => 6
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => 7
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => 8
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [5] => 6
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [6] => 7
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => 8
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => 8
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 9
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 9
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 8
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => 9
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => 7
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => 8
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => 9
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [5] => 6
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => 7
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 7
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => 8
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => 9
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5] => 6
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [6] => 7
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => 7
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => 8
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => 9
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5] => 6
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [6] => 7
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => 8
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => 9
[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
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => 10
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 10
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 9
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => 10
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => 8
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => 9
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => 10
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => 7
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => 8
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 8
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => 9
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => 10
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [6] => 7
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => 7
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => 8
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => 8
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => 9
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => 10
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5] => 6
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [6] => 7
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => 8
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => 7
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => 8
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => 9
[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] => [1,1,7] => 10
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [6] => 7
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => 8
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => 9
[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] => [1,8] => 10
[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
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => 10
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => 9
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => 10
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => 8
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => 9
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 9
>>> Load all 362 entries. <<<
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => 10
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6] => 7
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => 8
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => 8
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => 9
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => 9
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => 10
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6] => 7
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => 8
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 7
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => 8
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => 9
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => 8
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => 9
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => 10
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [6] => 7
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6] => 7
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => 8
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => 9
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => 8
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => 9
[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] => [1,8] => 10
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6] => 7
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => 8
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => 9
[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] => [9] => 10
[8,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => 10
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => 9
[7,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => 10
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => 10
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => 8
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => 9
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => 9
[6,3,1,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => 10
[6,2,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => 10
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => 8
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => 8
[5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => 9
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 8
[5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => 9
[5,3,1,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => 10
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => 9
[5,2,2,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => 10
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6] => 7
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => 8
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => 9
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => 8
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => 8
[4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => 9
[4,3,1,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 10
[4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => 9
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6] => 7
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => 8
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => 8
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => 9
[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] => [9] => 10
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => 8
[3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => 9
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => 8
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => 9
[2,2,2,1,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 10
[8,4] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => 10
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => 9
[7,4,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => 10
[7,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => 10
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => 8
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => 9
[6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => 9
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => 10
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 9
[6,2,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => 10
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => 8
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => 9
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => 8
[5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => 9
[5,4,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => 10
[5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => 9
[5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => 9
[5,3,2,1,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => 10
[5,2,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => 10
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6] => 7
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => 8
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => 8
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => 9
[4,4,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 10
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => 8
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => 9
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => 9
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => 9
[4,2,2,2,1,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => 10
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 7
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => 8
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => 9
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => 8
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => 9
[3,3,2,1,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 10
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => 9
[3,2,2,2,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => 10
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => 8
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => 9
[2,2,2,2,1,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 10
[8,5] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => 10
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => 9
[7,4,2] => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => 10
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => 10
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => 9
[6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => 9
[6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => 9
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => 8
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => 9
[5,5,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 10
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => 8
[5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => 9
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => 9
[5,4,2,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => 10
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => 9
[5,3,3,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => 10
[5,3,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => 10
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => 8
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => 8
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => 9
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => 9
[4,4,2,1,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => 10
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 8
[4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => 9
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => 9
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => 10
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => 8
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => 8
[3,3,3,2,1,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => 9
[3,3,3,1,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 10
[3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => 9
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => 9
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => 9
[2,2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => 10
[8,6] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => 10
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => 9
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 10
[7,5,2] => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => 10
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => 9
[6,6,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => 10
[6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => 9
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => 9
[6,3,3,2] => [1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => 10
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => 8
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => 9
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => 9
[5,5,2,1,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => 10
[5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => 9
[5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => 9
[5,4,3,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => 10
[5,4,2,2,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => 10
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 9
[5,3,3,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => 10
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => 8
[4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => 9
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => 8
[4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => 9
[4,4,3,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 10
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => 9
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => 9
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => 9
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => 8
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => 9
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => 9
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => 9
[3,2,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 10
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => 9
[2,2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => 10
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 10
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 10
[7,6,2] => [1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 10
[7,4,4] => [1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => 10
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => 9
[6,6,2,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => 10
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => 9
[6,4,4,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => 10
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => 10
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => 8
[5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => 9
[5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => 9
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => 9
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => 9
[5,4,3,2,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => 10
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => 8
[4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => 9
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => 9
[4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => 9
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => 9
[4,3,3,3,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => 10
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => 8
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => 9
[3,3,3,3,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => 10
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => 9
[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] => [1,8] => 10
[2,2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => 10
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 10
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 10
[6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => 9
[6,6,3,1] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => 10
[6,6,2,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => 10
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => 9
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => 9
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => 9
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => 9
[5,5,2,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => 10
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => 9
[5,3,3,3,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => 10
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 8
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => 9
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => 9
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => 9
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => 9
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => 10
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => 9
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => 9
[3,3,2,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 10
[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] => [9] => 10
[7,7,3] => [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => 10
[7,5,5] => [1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => 10
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => 9
[6,5,3,3] => [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 10
[6,4,4,3] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => 10
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => 9
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => 9
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 9
[5,3,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => 10
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => 9
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => 9
[4,4,4,3,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => 10
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => 9
[4,3,3,3,3,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => 10
[4,3,3,3,2,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => 10
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => 9
[3,3,3,3,3,1,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => 10
[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] => [9] => 10
[5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9] => 10
[5,5,4,3,1] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9] => 10
[4,3,3,3,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => 10
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => 10
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => 10
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => 9
[6,5,5,4] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => 10
[7,6,5] => [1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => 10
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => 9
[3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => 10
[3,3,3,3,3,2,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => 10
[4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => 10
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 9
[4,4,4,3,3,3] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 10
[4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => 10
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => 9
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => 10
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => 9
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => 10
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => 10
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => 10
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => 10
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 10
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => 10
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => 10
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Description
The semiperimeter of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the semiperimeter of the polygon determined by the axis and the bargraph. Put differently, it is the sum of the number of up steps and the number of horizontal steps when regarding the bargraph as a path with up, horizontal and down steps.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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.