Identifier
Values
[1,0] => [[1],[2]] => [[1],[2]] => 1
[1,0,1,0] => [[1,3],[2,4]] => [[1,2],[3,4]] => 1
[1,1,0,0] => [[1,2],[3,4]] => [[1,3],[2,4]] => 2
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [[1,2,4],[3,5,6]] => 2
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]] => 2
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]] => 2
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [[1,2,3],[4,5,6]] => 1
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [[1,3,5],[2,4,6]] => 3
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [[1,2,4,6],[3,5,7,8]] => 3
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [[1,2,4,7],[3,5,6,8]] => 3
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [[1,2,5,6],[3,4,7,8]] => 2
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [[1,2,4,5],[3,6,7,8]] => 2
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [[1,2,5,7],[3,4,6,8]] => 3
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [[1,3,4,6],[2,5,7,8]] => 3
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [[1,3,4,7],[2,5,6,8]] => 3
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [[1,2,3,6],[4,5,7,8]] => 2
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [[1,2,3,5],[4,6,7,8]] => 2
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [[1,3,5,6],[2,4,7,8]] => 3
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [[1,3,4,5],[2,6,7,8]] => 2
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [[1,2,3,4],[5,6,7,8]] => 1
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [[1,3,5,7],[2,4,6,8]] => 4
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,2,4,6,8],[3,5,7,9,10]] => 4
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [[1,2,4,7,8],[3,5,6,9,10]] => 3
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [[1,2,4,6,7],[3,5,8,9,10]] => 3
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [[1,2,5,6,8],[3,4,7,9,10]] => 3
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [[1,2,5,6,9],[3,4,7,8,10]] => 3
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [[1,2,4,5,8],[3,6,7,9,10]] => 3
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [[1,2,4,5,7],[3,6,8,9,10]] => 3
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [[1,2,4,5,9],[3,6,7,8,10]] => 3
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [[1,2,5,7,8],[3,4,6,9,10]] => 3
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [[1,2,5,6,7],[3,4,8,9,10]] => 2
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [[1,2,4,5,6],[3,7,8,9,10]] => 2
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [[1,2,3,6,8],[4,5,7,9,10]] => 3
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [[1,2,3,6,9],[4,5,7,8,10]] => 3
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [[1,2,3,5,8],[4,6,7,9,10]] => 3
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [[1,2,3,5,7],[4,6,8,9,10]] => 3
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [[1,2,3,5,9],[4,6,7,8,10]] => 3
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [[1,2,3,7,8],[4,5,6,9,10]] => 2
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [[1,2,3,6,7],[4,5,8,9,10]] => 2
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [[1,2,3,5,6],[4,7,8,9,10]] => 2
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [[1,2,3,7,9],[4,5,6,8,10]] => 3
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [[1,2,3,4,8],[5,6,7,9,10]] => 2
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [[1,2,3,4,7],[5,6,8,9,10]] => 2
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [[1,2,3,4,6],[5,7,8,9,10]] => 2
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [[1,3,4,5,6],[2,7,8,9,10]] => 2
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [[1,2,3,4,5],[6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
>>> Load all 233 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 6
[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]] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[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]] => [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,5,6,7,8,10],[3,4,9,11,12,13,14]] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,9,10],[3,6,8,11,12,13,14]] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[1,2,3,6,7,9,11],[4,5,8,10,12,13,14]] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[1,2,3,6,7,8,10],[4,5,9,11,12,13,14]] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,7,10,11],[4,6,8,9,12,13,14]] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,9,10],[4,6,8,11,12,13,14]] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,5,6,9,10],[4,7,8,11,12,13,14]] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,5,6,8,9],[4,7,10,11,12,13,14]] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[1,2,3,4,7,9,12],[5,6,8,10,11,13,14]] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[1,2,3,4,7,9,11],[5,6,8,10,12,13,14]] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[1,2,3,4,7,8,11],[5,6,9,10,12,13,14]] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[1,2,3,4,7,8,10],[5,6,9,11,12,13,14]] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,6,11,12],[5,7,8,9,10,13,14]] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,6,10,11],[5,7,8,9,12,13,14]] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,6,9,10],[5,7,8,11,12,13,14]] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,9],[5,7,10,11,12,13,14]] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => 3
[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]] => [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]] => 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]] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[1,2,3,4,5,8,11],[6,7,9,10,12,13,14]] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10],[6,7,9,11,12,13,14]] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,8],[6,9,10,11,12,13,14]] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9],[7,8,10,11,12,13,14]] => [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,10,11],[5,7,9,12,13,14,15,16]] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10,12],[6,7,9,11,13,14,15,16]] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,9,10],[6,8,11,12,13,14,15,16]] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9,11],[7,8,10,12,13,14,15,16]] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,9],[7,10,11,12,13,14,15,16]] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,10],[8,9,11,12,13,14,15,16]] => [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9,10],[8,11,12,13,14,15,16,17,18]] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,11],[9,10,12,13,14,15,16,17,18]] => [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,10,11],[9,12,13,14,15,16,17,18,19,20]] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,12],[10,11,13,14,15,16,17,18,19,20]] => [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,10,13],[11,12,14,15,16,17,18,19,20,21,22]] => [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]] => 2
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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
row-to-column-descents
Description
Return a standard tableau whose column descent set equals the row descent set of the original tableau.
A column descent in a standard tableau is an entry $i$ such that $i+1$ appears in a column to the left of the cell containing $i$, in English notation.
A row descent is an entry $i$ such that $i+1$ appears in a row above of the cell containing $i$.