Identifier
Values
[1,0] => [[1],[2]] => [[1,2]] => 0
[1,0,1,0] => [[1,3],[2,4]] => [[1,2,4],[3]] => 2
[1,1,0,0] => [[1,2],[3,4]] => [[1,2,3,4]] => 0
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => 6
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [[1,2,4,5,6],[3]] => 2
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [[1,2,3,4,6],[5]] => 4
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [[1,2,3,5,6],[4]] => 3
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 12
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [[1,2,4,6,7,8],[3,5]] => 6
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [[1,2,4,5,6,8],[3,7]] => 8
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [[1,2,4,5,7,8],[3,6]] => 7
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [[1,2,4,5,6,7,8],[3]] => 2
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [[1,2,3,4,6,8],[5,7]] => 10
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [[1,2,3,4,7,8],[5,6]] => 4
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [[1,2,3,5,6,8],[4,7]] => 9
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [[1,2,3,5,7,8],[4,6]] => 8
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [[1,2,3,5,6,7,8],[4]] => 3
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [[1,2,3,4,5,6,8],[7]] => 6
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [[1,2,3,4,5,7,8],[6]] => 5
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [[1,2,3,4,6,7,8],[5]] => 4
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,2,4,6,8,10],[3,5,7,9]] => 20
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [[1,2,4,6,8,9,10],[3,5,7]] => 12
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [[1,2,4,6,7,8,10],[3,5,9]] => 14
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [[1,2,4,6,7,9,10],[3,5,8]] => 13
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [[1,2,4,6,7,8,9,10],[3,5]] => 6
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [[1,2,4,5,6,8,10],[3,7,9]] => 16
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [[1,2,4,5,6,9,10],[3,7,8]] => 8
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [[1,2,4,5,7,8,10],[3,6,9]] => 15
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [[1,2,4,5,7,9,10],[3,6,8]] => 14
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [[1,2,4,5,7,8,9,10],[3,6]] => 7
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [[1,2,4,5,6,7,8,10],[3,9]] => 10
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [[1,2,4,5,6,7,9,10],[3,8]] => 9
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [[1,2,4,5,6,8,9,10],[3,7]] => 8
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [[1,2,4,5,6,7,8,9,10],[3]] => 2
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [[1,2,3,4,6,8,10],[5,7,9]] => 18
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [[1,2,3,4,6,9,10],[5,7,8]] => 10
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [[1,2,3,4,7,8,10],[5,6,9]] => 12
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [[1,2,3,4,7,9,10],[5,6,8]] => 11
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [[1,2,3,4,7,8,9,10],[5,6]] => 4
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [[1,2,3,5,6,8,10],[4,7,9]] => 17
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [[1,2,3,5,6,9,10],[4,7,8]] => 9
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [[1,2,3,5,7,8,10],[4,6,9]] => 16
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [[1,2,3,5,7,9,10],[4,6,8]] => 15
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [[1,2,3,5,7,8,9,10],[4,6]] => 8
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [[1,2,3,5,6,7,8,10],[4,9]] => 11
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [[1,2,3,5,6,7,9,10],[4,8]] => 10
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [[1,2,3,5,6,8,9,10],[4,7]] => 9
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [[1,2,3,5,6,7,8,9,10],[4]] => 3
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [[1,2,3,4,5,6,8,10],[7,9]] => 14
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [[1,2,3,4,5,6,9,10],[7,8]] => 6
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [[1,2,3,4,5,7,8,10],[6,9]] => 13
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [[1,2,3,4,5,7,9,10],[6,8]] => 12
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [[1,2,3,4,5,8,9,10],[6,7]] => 5
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [[1,2,3,4,6,7,8,10],[5,9]] => 12
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [[1,2,3,4,6,7,9,10],[5,8]] => 11
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [[1,2,3,4,6,8,9,10],[5,7]] => 10
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [[1,2,3,4,6,7,8,9,10],[5]] => 4
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [[1,2,3,4,5,6,7,8,10],[9]] => 8
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [[1,2,3,4,5,6,7,9,10],[8]] => 7
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [[1,2,3,4,5,6,8,9,10],[7]] => 6
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [[1,2,3,4,5,7,8,9,10],[6]] => 5
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => 30
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2,4,6,8,10,11,12],[3,5,7,9]] => 20
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,2,4,6,8,9,10,12],[3,5,7,11]] => 22
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2,4,6,8,9,11,12],[3,5,7,10]] => 21
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2,4,6,8,9,10,11,12],[3,5,7]] => 12
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,2,4,6,7,8,10,12],[3,5,9,11]] => 24
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2,4,6,7,8,11,12],[3,5,9,10]] => 14
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,2,4,6,7,9,10,12],[3,5,8,11]] => 23
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2,4,6,7,9,11,12],[3,5,8,10]] => 22
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2,4,6,7,9,10,11,12],[3,5,8]] => 13
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,2,4,6,7,8,9,10,12],[3,5,11]] => 16
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2,4,6,7,8,9,11,12],[3,5,10]] => 15
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2,4,6,7,8,10,11,12],[3,5,9]] => 14
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2,4,6,7,8,9,10,11,12],[3,5]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,2,4,5,6,8,10,12],[3,7,9,11]] => 26
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2,4,5,6,8,11,12],[3,7,9,10]] => 16
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,2,4,5,6,9,10,12],[3,7,8,11]] => 18
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2,4,5,6,9,11,12],[3,7,8,10]] => 17
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2,4,5,6,9,10,11,12],[3,7,8]] => 8
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,2,4,5,7,8,10,12],[3,6,9,11]] => 25
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2,4,5,7,8,11,12],[3,6,9,10]] => 15
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,2,4,5,7,9,10,12],[3,6,8,11]] => 24
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2,4,5,7,9,11,12],[3,6,8,10]] => 23
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2,4,5,7,9,10,11,12],[3,6,8]] => 14
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,2,4,5,7,8,9,10,12],[3,6,11]] => 17
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2,4,5,7,8,9,11,12],[3,6,10]] => 16
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2,4,5,7,8,10,11,12],[3,6,9]] => 15
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2,4,5,7,8,9,10,11,12],[3,6]] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,2,4,5,6,7,8,10,12],[3,9,11]] => 20
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2,4,5,6,7,8,11,12],[3,9,10]] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,2,4,5,6,7,9,10,12],[3,8,11]] => 19
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2,4,5,6,7,9,11,12],[3,8,10]] => 18
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2,4,5,6,7,10,11,12],[3,8,9]] => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,2,4,5,6,8,9,10,12],[3,7,11]] => 18
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2,4,5,6,8,9,11,12],[3,7,10]] => 17
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2,4,5,6,8,10,11,12],[3,7,9]] => 16
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2,4,5,6,8,9,10,11,12],[3,7]] => 8
>>> Load all 196 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]] => [[1,2,4,5,6,7,8,9,10,12],[3,11]] => 12
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => [[1,2,4,5,6,7,8,9,11,12],[3,10]] => 11
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => [[1,2,4,5,6,7,8,10,11,12],[3,9]] => 10
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => [[1,2,4,5,6,7,9,10,11,12],[3,8]] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => [[1,2,4,5,6,7,8,9,10,11,12],[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]] => [[1,2,3,4,6,8,10,12],[5,7,9,11]] => 28
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => [[1,2,3,4,6,8,11,12],[5,7,9,10]] => 18
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [[1,2,3,4,6,9,10,12],[5,7,8,11]] => 20
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [[1,2,3,4,6,9,11,12],[5,7,8,10]] => 19
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => [[1,2,3,4,6,9,10,11,12],[5,7,8]] => 10
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [[1,2,3,4,7,8,10,12],[5,6,9,11]] => 22
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [[1,2,3,4,7,8,11,12],[5,6,9,10]] => 12
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [[1,2,3,4,7,9,10,12],[5,6,8,11]] => 21
[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [[1,2,3,4,7,9,11,12],[5,6,8,10]] => 20
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [[1,2,3,4,7,9,10,11,12],[5,6,8]] => 11
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [[1,2,3,4,7,8,9,10,12],[5,6,11]] => 14
[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [[1,2,3,4,7,8,9,11,12],[5,6,10]] => 13
[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [[1,2,3,4,7,8,10,11,12],[5,6,9]] => 12
[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => [[1,2,3,4,7,8,9,10,11,12],[5,6]] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [[1,2,3,5,6,8,10,12],[4,7,9,11]] => 27
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [[1,2,3,5,6,8,11,12],[4,7,9,10]] => 17
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [[1,2,3,5,6,9,10,12],[4,7,8,11]] => 19
[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [[1,2,3,5,6,9,11,12],[4,7,8,10]] => 18
[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [[1,2,3,5,6,9,10,11,12],[4,7,8]] => 9
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [[1,2,3,5,7,8,10,12],[4,6,9,11]] => 26
[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [[1,2,3,5,7,8,11,12],[4,6,9,10]] => 16
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [[1,2,3,5,7,9,10,12],[4,6,8,11]] => 25
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [[1,2,3,5,7,9,11,12],[4,6,8,10]] => 24
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,2,3,5,7,9,10,11,12],[4,6,8]] => 15
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [[1,2,3,5,7,8,9,10,12],[4,6,11]] => 18
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,2,3,5,7,8,9,11,12],[4,6,10]] => 17
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,2,3,5,7,8,10,11,12],[4,6,9]] => 16
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [[1,2,3,5,7,8,9,10,11,12],[4,6]] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [[1,2,3,5,6,7,8,10,12],[4,9,11]] => 21
[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [[1,2,3,5,6,7,8,11,12],[4,9,10]] => 11
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [[1,2,3,5,6,7,9,10,12],[4,8,11]] => 20
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,2,3,5,6,7,9,11,12],[4,8,10]] => 19
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [[1,2,3,5,6,7,10,11,12],[4,8,9]] => 10
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [[1,2,3,5,6,8,9,10,12],[4,7,11]] => 19
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,2,3,5,6,8,9,11,12],[4,7,10]] => 18
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,2,3,5,6,8,10,11,12],[4,7,9]] => 17
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [[1,2,3,5,6,8,9,10,11,12],[4,7]] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [[1,2,3,5,6,7,8,9,10,12],[4,11]] => 13
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [[1,2,3,5,6,7,8,9,11,12],[4,10]] => 12
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [[1,2,3,5,6,7,8,10,11,12],[4,9]] => 11
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [[1,2,3,5,6,7,9,10,11,12],[4,8]] => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => [[1,2,3,5,6,7,8,9,10,11,12],[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]] => [[1,2,3,4,5,6,8,10,12],[7,9,11]] => 24
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => [[1,2,3,4,5,6,8,11,12],[7,9,10]] => 14
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => [[1,2,3,4,5,6,9,10,12],[7,8,11]] => 16
[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => [[1,2,3,4,5,6,9,11,12],[7,8,10]] => 15
[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => [[1,2,3,4,5,6,10,11,12],[7,8,9]] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => [[1,2,3,4,5,7,8,10,12],[6,9,11]] => 23
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => [[1,2,3,4,5,7,8,11,12],[6,9,10]] => 13
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => [[1,2,3,4,5,7,9,10,12],[6,8,11]] => 22
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,2,3,4,5,7,9,11,12],[6,8,10]] => 21
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => [[1,2,3,4,5,7,10,11,12],[6,8,9]] => 12
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => [[1,2,3,4,5,8,9,10,12],[6,7,11]] => 15
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => [[1,2,3,4,5,8,9,11,12],[6,7,10]] => 14
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => [[1,2,3,4,5,8,10,11,12],[6,7,9]] => 13
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => [[1,2,3,4,5,8,9,10,11,12],[6,7]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => [[1,2,3,4,6,7,8,10,12],[5,9,11]] => 22
[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => [[1,2,3,4,6,7,8,11,12],[5,9,10]] => 12
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => [[1,2,3,4,6,7,9,10,12],[5,8,11]] => 21
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,2,3,4,6,7,9,11,12],[5,8,10]] => 20
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => [[1,2,3,4,6,7,10,11,12],[5,8,9]] => 11
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => [[1,2,3,4,6,8,9,10,12],[5,7,11]] => 20
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,2,3,4,6,8,9,11,12],[5,7,10]] => 19
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,2,3,4,6,8,10,11,12],[5,7,9]] => 18
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => [[1,2,3,4,6,8,9,10,11,12],[5,7]] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => [[1,2,3,4,6,7,8,9,10,12],[5,11]] => 14
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => [[1,2,3,4,6,7,8,9,11,12],[5,10]] => 13
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => [[1,2,3,4,6,7,8,10,11,12],[5,9]] => 12
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => [[1,2,3,4,6,7,9,10,11,12],[5,8]] => 11
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => [[1,2,3,4,6,7,8,9,10,11,12],[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]] => [[1,2,3,4,5,6,7,8,10,12],[9,11]] => 18
[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => [[1,2,3,4,5,6,7,8,11,12],[9,10]] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => [[1,2,3,4,5,6,7,9,10,12],[8,11]] => 17
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => [[1,2,3,4,5,6,7,9,11,12],[8,10]] => 16
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => [[1,2,3,4,5,6,7,10,11,12],[8,9]] => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => [[1,2,3,4,5,6,8,9,10,12],[7,11]] => 16
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => [[1,2,3,4,5,6,8,9,11,12],[7,10]] => 15
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => [[1,2,3,4,5,6,8,10,11,12],[7,9]] => 14
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => [[1,2,3,4,5,6,9,10,11,12],[7,8]] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => [[1,2,3,4,5,7,8,9,10,12],[6,11]] => 15
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => [[1,2,3,4,5,7,8,9,11,12],[6,10]] => 14
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => [[1,2,3,4,5,7,8,10,11,12],[6,9]] => 13
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => [[1,2,3,4,5,7,9,10,11,12],[6,8]] => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => [[1,2,3,4,5,7,8,9,10,11,12],[6]] => 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]] => [[1,2,3,4,5,6,7,8,9,10,12],[11]] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => [[1,2,3,4,5,6,7,8,9,11,12],[10]] => 9
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => [[1,2,3,4,5,6,7,8,10,11,12],[9]] => 8
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => [[1,2,3,4,5,6,7,9,10,11,12],[8]] => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => [[1,2,3,4,5,6,8,9,10,11,12],[7]] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0
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Description
The (standard) major index of a standard tableau.
A descent of a standard tableau $T$ is an index $i$ such that $i+1$ appears in a row strictly below the row of $i$. The (standard) major index is the the sum of the descents.
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
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).