Identifier
Values
[1] => [1,0,1,0] => [[1,3],[2,4]] => 2
[2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 2
[1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 2
[3] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 3
[2,2] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 3
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => 3
[3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 3
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]] => 2
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => 2
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => 3
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 3
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => 3
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => 3
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]] => 2
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => 2
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => 3
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => 3
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 3
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 3
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 3
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[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] => [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]] => 2
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => 2
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]] => 3
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]] => 3
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => 3
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => 3
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 3
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 3
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[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] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[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] => [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]] => 2
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]] => 2
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]] => 3
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]] => 3
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => 3
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]] => 3
>>> Load all 185 entries. <<<
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 3
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => 3
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 3
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]] => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 3
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[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] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[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] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[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] => [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => 4
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 4
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => 5
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 4
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => 3
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 4
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => 4
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => 3
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => 4
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => 4
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 5
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => 4
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => 4
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 4
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => 5
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => 4
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 5
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => 4
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => 4
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => 5
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => 4
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 4
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => 4
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => 5
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => 5
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => 5
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => 5
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => 5
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 6
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Description
The number of descents of a standard tableau.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.