- FindStat

Identifier

Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions

Images

[1,0] => [[1],[2]] => {{1},{2}} => {{1},{2}}

[1,0,1,0] => [[1,3],[2,4]] => {{1,3},{2,4}} => {{1,4},{2,3}}

[1,1,0,0] => [[1,2],[3,4]] => {{1,2},{3,4}} => {{1,2},{3,4}}

[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => {{1,6},{2,3,4,5}}

[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => {{1,4},{2,3,5,6}}

[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => {{1,2,4,5},{3,6}}

[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => {{1,2,5,6},{3,4}}

[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}

[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => {{1,3,5,7},{2,4,6,8}} => {{1,8},{2,3,4,5,6,7}}

[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => {{1,3,5,6},{2,4,7,8}} => {{1,6},{2,3,4,5,7,8}}

[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => {{1,3,4,7},{2,5,6,8}} => {{1,4,5,8},{2,3,6,7}}

[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => {{1,3,4,6},{2,5,7,8}} => {{1,4,5,6},{2,3,7,8}}

[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => {{1,3,4,5},{2,6,7,8}} => {{1,4,6,7,8},{2,3,5}}

[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => {{1,2,5,7},{3,4,6,8}} => {{1,2,4,5,6,7},{3,8}}

[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => {{1,2,5,6},{3,4,7,8}} => {{1,2,4,5,7,8},{3,6}}

[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => {{1,2,4,7},{3,5,6,8}} => {{1,2,6,7},{3,4,5,8}}

[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => {{1,2,4,6},{3,5,7,8}} => {{1,2,7,8},{3,4,5,6}}

[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => {{1,2,4,5},{3,6,7,8}} => {{1,2,5},{3,4,6,7,8}}

[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => {{1,2,3,7},{4,5,6,8}} => {{1,2,3,5,8},{4,6,7}}

[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => {{1,2,3,6},{4,5,7,8}} => {{1,2,3,5,6},{4,7,8}}

[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,6,7,8},{4,5}}

[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}

[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => {{1,3,5,7,9},{2,4,6,8,10}} => {{1,10},{2,3,4,5,6,7,8,9}}

[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => {{1,3,5,7,8},{2,4,6,9,10}} => {{1,8},{2,3,4,5,6,7,9,10}}

[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => {{1,3,5,6,9},{2,4,7,8,10}} => {{1,6,7,10},{2,3,4,5,8,9}}

[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => {{1,3,5,6,8},{2,4,7,9,10}} => {{1,6,7,8},{2,3,4,5,9,10}}

[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => {{1,3,5,6,7},{2,4,8,9,10}} => {{1,6,8,9,10},{2,3,4,5,7}}

[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => {{1,3,4,7,9},{2,5,6,8,10}} => {{1,4,5,10},{2,3,6,7,8,9}}

[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => {{1,3,4,7,8},{2,5,6,9,10}} => {{1,4,5,8},{2,3,6,7,9,10}}

[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => {{1,3,4,6,9},{2,5,7,8,10}} => {{1,4,5,6,7,10},{2,3,8,9}}

[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => {{1,3,4,6,8},{2,5,7,9,10}} => {{1,4,5,6,7,8},{2,3,9,10}}

[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => {{1,3,4,6,7},{2,5,8,9,10}} => {{1,4,5,6,8,9,10},{2,3,7}}

[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => {{1,3,4,5,9},{2,6,7,8,10}} => {{1,4,7,10},{2,3,5,6,8,9}}

[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => {{1,3,4,5,8},{2,6,7,9,10}} => {{1,4,7,8},{2,3,5,6,9,10}}

[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => {{1,3,4,5,7},{2,6,8,9,10}} => {{1,4,8,9,10},{2,3,5,6,7}}

[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => {{1,3,4,5,6},{2,7,8,9,10}} => {{1,4,6},{2,3,5,7,8,9,10}}

[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => {{1,2,5,7,9},{3,4,6,8,10}} => {{1,2,4,5,6,7,8,9},{3,10}}

[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => {{1,2,5,7,8},{3,4,6,9,10}} => {{1,2,4,5,6,7,9,10},{3,8}}

[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => {{1,2,5,6,9},{3,4,7,8,10}} => {{1,2,4,5,8,9},{3,6,7,10}}

[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => {{1,2,5,6,8},{3,4,7,9,10}} => {{1,2,4,5,9,10},{3,6,7,8}}

[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => {{1,2,5,6,7},{3,4,8,9,10}} => {{1,2,4,5,7},{3,6,8,9,10}}

[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => {{1,2,4,7,9},{3,5,6,8,10}} => {{1,2,6,7,8,9},{3,4,5,10}}

[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => {{1,2,4,7,8},{3,5,6,9,10}} => {{1,2,6,7,9,10},{3,4,5,8}}

[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => {{1,2,4,6,9},{3,5,7,8,10}} => {{1,2,8,9},{3,4,5,6,7,10}}

[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => {{1,2,4,6,8},{3,5,7,9,10}} => {{1,2,9,10},{3,4,5,6,7,8}}

[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => {{1,2,4,6,7},{3,5,8,9,10}} => {{1,2,7},{3,4,5,6,8,9,10}}

[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => {{1,2,4,5,9},{3,6,7,8,10}} => {{1,2,5,6,8,9},{3,4,7,10}}

[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => {{1,2,4,5,8},{3,6,7,9,10}} => {{1,2,5,6,9,10},{3,4,7,8}}

[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => {{1,2,4,5,7},{3,6,8,9,10}} => {{1,2,5,6,7},{3,4,8,9,10}}

[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => {{1,2,4,5,6},{3,7,8,9,10}} => {{1,2,5,7,8,9,10},{3,4,6}}

[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => {{1,2,3,7,9},{4,5,6,8,10}} => {{1,2,3,5,10},{4,6,7,8,9}}

[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => {{1,2,3,7,8},{4,5,6,9,10}} => {{1,2,3,5,8},{4,6,7,9,10}}

[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => {{1,2,3,6,9},{4,5,7,8,10}} => {{1,2,3,5,6,7,10},{4,8,9}}

[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => {{1,2,3,6,8},{4,5,7,9,10}} => {{1,2,3,5,6,7,8},{4,9,10}}

[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => {{1,2,3,6,7},{4,5,8,9,10}} => {{1,2,3,5,6,8,9,10},{4,7}}

[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => {{1,2,3,5,9},{4,6,7,8,10}} => {{1,2,3,7,10},{4,5,6,8,9}}

[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => {{1,2,3,5,8},{4,6,7,9,10}} => {{1,2,3,7,8},{4,5,6,9,10}}

[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => {{1,2,3,5,7},{4,6,8,9,10}} => {{1,2,3,8,9,10},{4,5,6,7}}

[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => {{1,2,3,5,6},{4,7,8,9,10}} => {{1,2,3,6},{4,5,7,8,9,10}}

[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => {{1,2,3,4,9},{5,6,7,8,10}} => {{1,2,3,4,6,8,9},{5,7,10}}

[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => {{1,2,3,4,8},{5,6,7,9,10}} => {{1,2,3,4,6,9,10},{5,7,8}}

[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => {{1,2,3,4,7},{5,6,8,9,10}} => {{1,2,3,4,6,7},{5,8,9,10}}

[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => {{1,2,3,4,6},{5,7,8,9,10}} => {{1,2,3,4,7,8,9,10},{5,6}}

[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}} => {{1,2,3,4,5},{6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => {{1,3,5,7,9,11},{2,4,6,8,10,12}} => {{1,12},{2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => {{1,3,5,7,9,10},{2,4,6,8,11,12}} => {{1,10},{2,3,4,5,6,7,8,9,11,12}}

[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => {{1,3,5,7,8,11},{2,4,6,9,10,12}} => {{1,8,9,12},{2,3,4,5,6,7,10,11}}

[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => {{1,3,5,7,8,10},{2,4,6,9,11,12}} => {{1,8,9,10},{2,3,4,5,6,7,11,12}}

[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => {{1,3,5,7,8,9},{2,4,6,10,11,12}} => {{1,8,10,11,12},{2,3,4,5,6,7,9}}

[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => {{1,3,5,6,9,11},{2,4,7,8,10,12}} => {{1,6,7,12},{2,3,4,5,8,9,10,11}}

[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => {{1,3,5,6,9,10},{2,4,7,8,11,12}} => {{1,6,7,10},{2,3,4,5,8,9,11,12}}

[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => {{1,3,5,6,8,11},{2,4,7,9,10,12}} => {{1,6,7,8,9,12},{2,3,4,5,10,11}}

[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => {{1,3,5,6,8,10},{2,4,7,9,11,12}} => {{1,6,7,8,9,10},{2,3,4,5,11,12}}

[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => {{1,3,5,6,8,9},{2,4,7,10,11,12}} => {{1,6,7,8,10,11,12},{2,3,4,5,9}}

[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => {{1,3,5,6,7,11},{2,4,8,9,10,12}} => {{1,6,9,12},{2,3,4,5,7,8,10,11}}

[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => {{1,3,5,6,7,10},{2,4,8,9,11,12}} => {{1,6,9,10},{2,3,4,5,7,8,11,12}}

[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => {{1,3,5,6,7,9},{2,4,8,10,11,12}} => {{1,6,10,11,12},{2,3,4,5,7,8,9}}

[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => {{1,3,5,6,7,8},{2,4,9,10,11,12}} => {{1,6,8},{2,3,4,5,7,9,10,11,12}}

[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => {{1,3,4,7,9,11},{2,5,6,8,10,12}} => {{1,4,5,12},{2,3,6,7,8,9,10,11}}

[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => {{1,3,4,7,9,10},{2,5,6,8,11,12}} => {{1,4,5,10},{2,3,6,7,8,9,11,12}}

[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => {{1,3,4,7,8,11},{2,5,6,9,10,12}} => {{1,4,5,8,9,12},{2,3,6,7,10,11}}

[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => {{1,3,4,7,8,10},{2,5,6,9,11,12}} => {{1,4,5,8,9,10},{2,3,6,7,11,12}}

[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => {{1,3,4,7,8,9},{2,5,6,10,11,12}} => {{1,4,5,8,10,11,12},{2,3,6,7,9}}

[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => {{1,3,4,6,9,11},{2,5,7,8,10,12}} => {{1,4,5,6,7,12},{2,3,8,9,10,11}}

[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => {{1,3,4,6,9,10},{2,5,7,8,11,12}} => {{1,4,5,6,7,10},{2,3,8,9,11,12}}

[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => {{1,3,4,6,8,11},{2,5,7,9,10,12}} => {{1,4,5,6,7,8,9,12},{2,3,10,11}}

[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => {{1,3,4,6,8,10},{2,5,7,9,11,12}} => {{1,4,5,6,7,8,9,10},{2,3,11,12}}

[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => {{1,3,4,6,8,9},{2,5,7,10,11,12}} => {{1,4,5,6,7,8,10,11,12},{2,3,9}}

[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => {{1,3,4,6,7,11},{2,5,8,9,10,12}} => {{1,4,5,6,9,12},{2,3,7,8,10,11}}

[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => {{1,3,4,6,7,10},{2,5,8,9,11,12}} => {{1,4,5,6,9,10},{2,3,7,8,11,12}}

[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => {{1,3,4,6,7,9},{2,5,8,10,11,12}} => {{1,4,5,6,10,11,12},{2,3,7,8,9}}

[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => {{1,3,4,6,7,8},{2,5,9,10,11,12}} => {{1,4,5,6,8},{2,3,7,9,10,11,12}}

[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => {{1,3,4,5,9,11},{2,6,7,8,10,12}} => {{1,4,7,12},{2,3,5,6,8,9,10,11}}

[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => {{1,3,4,5,9,10},{2,6,7,8,11,12}} => {{1,4,7,10},{2,3,5,6,8,9,11,12}}

[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => {{1,3,4,5,8,11},{2,6,7,9,10,12}} => {{1,4,7,8,9,12},{2,3,5,6,10,11}}

[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => {{1,3,4,5,8,10},{2,6,7,9,11,12}} => {{1,4,7,8,9,10},{2,3,5,6,11,12}}

[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => {{1,3,4,5,8,9},{2,6,7,10,11,12}} => {{1,4,7,8,10,11,12},{2,3,5,6,9}}

[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => {{1,3,4,5,7,11},{2,6,8,9,10,12}} => {{1,4,9,12},{2,3,5,6,7,8,10,11}}

[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => {{1,3,4,5,7,10},{2,6,8,9,11,12}} => {{1,4,9,10},{2,3,5,6,7,8,11,12}}

[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => {{1,3,4,5,7,9},{2,6,8,10,11,12}} => {{1,4,10,11,12},{2,3,5,6,7,8,9}}

[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => {{1,3,4,5,7,8},{2,6,9,10,11,12}} => {{1,4,8},{2,3,5,6,7,9,10,11,12}}

>>> 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]] => {{1,3,4,5,6,11},{2,7,8,9,10,12}} => {{1,4,6,7,9,12},{2,3,5,8,10,11}}

[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => {{1,3,4,5,6,10},{2,7,8,9,11,12}} => {{1,4,6,7,9,10},{2,3,5,8,11,12}}

[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => {{1,3,4,5,6,9},{2,7,8,10,11,12}} => {{1,4,6,7,10,11,12},{2,3,5,8,9}}

[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => {{1,3,4,5,6,8},{2,7,9,10,11,12}} => {{1,4,6,7,8},{2,3,5,9,10,11,12}}

[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => {{1,3,4,5,6,7},{2,8,9,10,11,12}} => {{1,4,6,8,9,10,11,12},{2,3,5,7}}

[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => {{1,2,5,7,9,11},{3,4,6,8,10,12}} => {{1,2,4,5,6,7,8,9,10,11},{3,12}}

[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => {{1,2,5,7,9,10},{3,4,6,8,11,12}} => {{1,2,4,5,6,7,8,9,11,12},{3,10}}

[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => {{1,2,5,7,8,11},{3,4,6,9,10,12}} => {{1,2,4,5,6,7,10,11},{3,8,9,12}}

[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => {{1,2,5,7,8,10},{3,4,6,9,11,12}} => {{1,2,4,5,6,7,11,12},{3,8,9,10}}

[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => {{1,2,5,7,8,9},{3,4,6,10,11,12}} => {{1,2,4,5,6,7,9},{3,8,10,11,12}}

[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => {{1,2,5,6,9,11},{3,4,7,8,10,12}} => {{1,2,4,5,8,9,10,11},{3,6,7,12}}

[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => {{1,2,5,6,9,10},{3,4,7,8,11,12}} => {{1,2,4,5,8,9,11,12},{3,6,7,10}}

[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => {{1,2,5,6,8,11},{3,4,7,9,10,12}} => {{1,2,4,5,10,11},{3,6,7,8,9,12}}

[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => {{1,2,5,6,8,10},{3,4,7,9,11,12}} => {{1,2,4,5,11,12},{3,6,7,8,9,10}}

[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => {{1,2,5,6,8,9},{3,4,7,10,11,12}} => {{1,2,4,5,9},{3,6,7,8,10,11,12}}

[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => {{1,2,5,6,7,11},{3,4,8,9,10,12}} => {{1,2,4,5,7,8,10,11},{3,6,9,12}}

[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => {{1,2,5,6,7,10},{3,4,8,9,11,12}} => {{1,2,4,5,7,8,11,12},{3,6,9,10}}

[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => {{1,2,5,6,7,9},{3,4,8,10,11,12}} => {{1,2,4,5,7,8,9},{3,6,10,11,12}}

[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => {{1,2,5,6,7,8},{3,4,9,10,11,12}} => {{1,2,4,5,7,9,10,11,12},{3,6,8}}

[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => {{1,2,4,7,9,11},{3,5,6,8,10,12}} => {{1,2,6,7,8,9,10,11},{3,4,5,12}}

[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => {{1,2,4,7,9,10},{3,5,6,8,11,12}} => {{1,2,6,7,8,9,11,12},{3,4,5,10}}

[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => {{1,2,4,7,8,11},{3,5,6,9,10,12}} => {{1,2,6,7,10,11},{3,4,5,8,9,12}}

[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => {{1,2,4,7,8,10},{3,5,6,9,11,12}} => {{1,2,6,7,11,12},{3,4,5,8,9,10}}

[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => {{1,2,4,7,8,9},{3,5,6,10,11,12}} => {{1,2,6,7,9},{3,4,5,8,10,11,12}}

[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => {{1,2,4,6,9,11},{3,5,7,8,10,12}} => {{1,2,8,9,10,11},{3,4,5,6,7,12}}

[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => {{1,2,4,6,9,10},{3,5,7,8,11,12}} => {{1,2,8,9,11,12},{3,4,5,6,7,10}}

[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => {{1,2,4,6,8,11},{3,5,7,9,10,12}} => {{1,2,10,11},{3,4,5,6,7,8,9,12}}

[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => {{1,2,4,6,8,10},{3,5,7,9,11,12}} => {{1,2,11,12},{3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => {{1,2,4,6,8,9},{3,5,7,10,11,12}} => {{1,2,9},{3,4,5,6,7,8,10,11,12}}

[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => {{1,2,4,6,7,11},{3,5,8,9,10,12}} => {{1,2,7,8,10,11},{3,4,5,6,9,12}}

[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => {{1,2,4,6,7,10},{3,5,8,9,11,12}} => {{1,2,7,8,11,12},{3,4,5,6,9,10}}

[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => {{1,2,4,6,7,9},{3,5,8,10,11,12}} => {{1,2,7,8,9},{3,4,5,6,10,11,12}}

[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => {{1,2,4,6,7,8},{3,5,9,10,11,12}} => {{1,2,7,9,10,11,12},{3,4,5,6,8}}

[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => {{1,2,4,5,9,11},{3,6,7,8,10,12}} => {{1,2,5,6,8,9,10,11},{3,4,7,12}}

[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => {{1,2,4,5,9,10},{3,6,7,8,11,12}} => {{1,2,5,6,8,9,11,12},{3,4,7,10}}

[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => {{1,2,4,5,8,11},{3,6,7,9,10,12}} => {{1,2,5,6,10,11},{3,4,7,8,9,12}}

[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => {{1,2,4,5,8,10},{3,6,7,9,11,12}} => {{1,2,5,6,11,12},{3,4,7,8,9,10}}

[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => {{1,2,4,5,8,9},{3,6,7,10,11,12}} => {{1,2,5,6,9},{3,4,7,8,10,11,12}}

[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => {{1,2,4,5,7,11},{3,6,8,9,10,12}} => {{1,2,5,6,7,8,10,11},{3,4,9,12}}

[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => {{1,2,4,5,7,10},{3,6,8,9,11,12}} => {{1,2,5,6,7,8,11,12},{3,4,9,10}}

[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => {{1,2,4,5,7,9},{3,6,8,10,11,12}} => {{1,2,5,6,7,8,9},{3,4,10,11,12}}

[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => {{1,2,4,5,7,8},{3,6,9,10,11,12}} => {{1,2,5,6,7,9,10,11,12},{3,4,8}}

[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => {{1,2,4,5,6,11},{3,7,8,9,10,12}} => {{1,2,5,8,10,11},{3,4,6,7,9,12}}

[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => {{1,2,4,5,6,10},{3,7,8,9,11,12}} => {{1,2,5,8,11,12},{3,4,6,7,9,10}}

[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => {{1,2,4,5,6,9},{3,7,8,10,11,12}} => {{1,2,5,8,9},{3,4,6,7,10,11,12}}

[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => {{1,2,4,5,6,8},{3,7,9,10,11,12}} => {{1,2,5,9,10,11,12},{3,4,6,7,8}}

[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => {{1,2,4,5,6,7},{3,8,9,10,11,12}} => {{1,2,5,7},{3,4,6,8,9,10,11,12}}

[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => {{1,2,3,7,9,11},{4,5,6,8,10,12}} => {{1,2,3,5,12},{4,6,7,8,9,10,11}}

[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => {{1,2,3,7,9,10},{4,5,6,8,11,12}} => {{1,2,3,5,10},{4,6,7,8,9,11,12}}

[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => {{1,2,3,7,8,11},{4,5,6,9,10,12}} => {{1,2,3,5,8,9,12},{4,6,7,10,11}}

[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => {{1,2,3,7,8,10},{4,5,6,9,11,12}} => {{1,2,3,5,8,9,10},{4,6,7,11,12}}

[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => {{1,2,3,7,8,9},{4,5,6,10,11,12}} => {{1,2,3,5,8,10,11,12},{4,6,7,9}}

[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => {{1,2,3,6,9,11},{4,5,7,8,10,12}} => {{1,2,3,5,6,7,12},{4,8,9,10,11}}

[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => {{1,2,3,6,9,10},{4,5,7,8,11,12}} => {{1,2,3,5,6,7,10},{4,8,9,11,12}}

[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => {{1,2,3,6,8,11},{4,5,7,9,10,12}} => {{1,2,3,5,6,7,8,9,12},{4,10,11}}

[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => {{1,2,3,6,8,10},{4,5,7,9,11,12}} => {{1,2,3,5,6,7,8,9,10},{4,11,12}}

[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => {{1,2,3,6,8,9},{4,5,7,10,11,12}} => {{1,2,3,5,6,7,8,10,11,12},{4,9}}

[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => {{1,2,3,6,7,11},{4,5,8,9,10,12}} => {{1,2,3,5,6,9,12},{4,7,8,10,11}}

[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => {{1,2,3,6,7,10},{4,5,8,9,11,12}} => {{1,2,3,5,6,9,10},{4,7,8,11,12}}

[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => {{1,2,3,6,7,9},{4,5,8,10,11,12}} => {{1,2,3,5,6,10,11,12},{4,7,8,9}}

[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => {{1,2,3,6,7,8},{4,5,9,10,11,12}} => {{1,2,3,5,6,8},{4,7,9,10,11,12}}

[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => {{1,2,3,5,9,11},{4,6,7,8,10,12}} => {{1,2,3,7,12},{4,5,6,8,9,10,11}}

[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => {{1,2,3,5,9,10},{4,6,7,8,11,12}} => {{1,2,3,7,10},{4,5,6,8,9,11,12}}

[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => {{1,2,3,5,8,11},{4,6,7,9,10,12}} => {{1,2,3,7,8,9,12},{4,5,6,10,11}}

[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => {{1,2,3,5,8,10},{4,6,7,9,11,12}} => {{1,2,3,7,8,9,10},{4,5,6,11,12}}

[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => {{1,2,3,5,8,9},{4,6,7,10,11,12}} => {{1,2,3,7,8,10,11,12},{4,5,6,9}}

[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => {{1,2,3,5,7,11},{4,6,8,9,10,12}} => {{1,2,3,9,12},{4,5,6,7,8,10,11}}

[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => {{1,2,3,5,7,10},{4,6,8,9,11,12}} => {{1,2,3,9,10},{4,5,6,7,8,11,12}}

[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => {{1,2,3,5,7,9},{4,6,8,10,11,12}} => {{1,2,3,10,11,12},{4,5,6,7,8,9}}

[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => {{1,2,3,5,7,8},{4,6,9,10,11,12}} => {{1,2,3,8},{4,5,6,7,9,10,11,12}}

[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => {{1,2,3,5,6,11},{4,7,8,9,10,12}} => {{1,2,3,6,7,9,12},{4,5,8,10,11}}

[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => {{1,2,3,5,6,10},{4,7,8,9,11,12}} => {{1,2,3,6,7,9,10},{4,5,8,11,12}}

[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => {{1,2,3,5,6,9},{4,7,8,10,11,12}} => {{1,2,3,6,7,10,11,12},{4,5,8,9}}

[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => {{1,2,3,5,6,8},{4,7,9,10,11,12}} => {{1,2,3,6,7,8},{4,5,9,10,11,12}}

[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => {{1,2,3,5,6,7},{4,8,9,10,11,12}} => {{1,2,3,6,8,9,10,11,12},{4,5,7}}

[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => {{1,2,3,4,9,11},{5,6,7,8,10,12}} => {{1,2,3,4,6,8,9,10,11},{5,7,12}}

[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => {{1,2,3,4,9,10},{5,6,7,8,11,12}} => {{1,2,3,4,6,8,9,11,12},{5,7,10}}

[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => {{1,2,3,4,8,11},{5,6,7,9,10,12}} => {{1,2,3,4,6,10,11},{5,7,8,9,12}}

[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => {{1,2,3,4,8,10},{5,6,7,9,11,12}} => {{1,2,3,4,6,11,12},{5,7,8,9,10}}

[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => {{1,2,3,4,8,9},{5,6,7,10,11,12}} => {{1,2,3,4,6,9},{5,7,8,10,11,12}}

[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => {{1,2,3,4,7,11},{5,6,8,9,10,12}} => {{1,2,3,4,6,7,8,10,11},{5,9,12}}

[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => {{1,2,3,4,7,10},{5,6,8,9,11,12}} => {{1,2,3,4,6,7,8,11,12},{5,9,10}}

[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => {{1,2,3,4,7,9},{5,6,8,10,11,12}} => {{1,2,3,4,6,7,8,9},{5,10,11,12}}

[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => {{1,2,3,4,7,8},{5,6,9,10,11,12}} => {{1,2,3,4,6,7,9,10,11,12},{5,8}}

[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => {{1,2,3,4,6,11},{5,7,8,9,10,12}} => {{1,2,3,4,8,10,11},{5,6,7,9,12}}

[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => {{1,2,3,4,6,10},{5,7,8,9,11,12}} => {{1,2,3,4,8,11,12},{5,6,7,9,10}}

[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => {{1,2,3,4,6,9},{5,7,8,10,11,12}} => {{1,2,3,4,8,9},{5,6,7,10,11,12}}

[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => {{1,2,3,4,6,8},{5,7,9,10,11,12}} => {{1,2,3,4,9,10,11,12},{5,6,7,8}}

[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => {{1,2,3,4,6,7},{5,8,9,10,11,12}} => {{1,2,3,4,7},{5,6,8,9,10,11,12}}

[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => {{1,2,3,4,5,11},{6,7,8,9,10,12}} => {{1,2,3,4,5,7,9,12},{6,8,10,11}}

[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => {{1,2,3,4,5,10},{6,7,8,9,11,12}} => {{1,2,3,4,5,7,9,10},{6,8,11,12}}

[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => {{1,2,3,4,5,9},{6,7,8,10,11,12}} => {{1,2,3,4,5,7,10,11,12},{6,8,9}}

[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => {{1,2,3,4,5,8},{6,7,9,10,11,12}} => {{1,2,3,4,5,7,8},{6,9,10,11,12}}

[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => {{1,2,3,4,5,7},{6,8,9,10,11,12}} => {{1,2,3,4,5,8,9,10,11,12},{6,7}}

[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}} => {{1,2,3,4,5,6},{7,8,9,10,11,12}}

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

rows

Description

The set partition whose blocks are the rows of the tableau.

Map

Kasraoui-Zeng

Description

The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.