Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
Images
[1] => [1,0] => {{1}} => [1]
[1,1] => [1,0,1,0] => {{1},{2}} => [1,1]
[2] => [1,1,0,0] => {{1,2}} => [2]
[1,1,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => [1,1,1]
[1,2] => [1,0,1,1,0,0] => {{1},{2,3}} => [2,1]
[2,1] => [1,1,0,0,1,0] => {{1,2},{3}} => [2,1]
[3] => [1,1,1,0,0,0] => {{1,2,3}} => [3]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => [1,1,1,1]
[1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => [2,1,1]
[1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => [2,1,1]
[1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => [3,1]
[2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => [2,1,1]
[2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => [2,2]
[3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => [3,1]
[4] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => [4]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => [1,1,1,1,1]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => [2,1,1,1]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => [2,1,1,1]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => [3,1,1]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => [2,1,1,1]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => [2,2,1]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => [3,1,1]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => [4,1]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => [2,1,1,1]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => [2,2,1]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => [2,2,1]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => [3,2]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => [3,1,1]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => [3,2]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => [4,1]
[5] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => [5]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => [2,1,1,1,1]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => [2,1,1,1,1]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => [3,1,1,1]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => [2,1,1,1,1]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => [2,2,1,1]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => [3,1,1,1]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => [4,1,1]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => [2,1,1,1,1]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => [2,2,1,1]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => [2,2,1,1]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => [3,2,1]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => [3,1,1,1]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => [3,2,1]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => [4,1,1]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => [5,1]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => [2,1,1,1,1]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => [2,2,1,1]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => [2,2,1,1]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => [3,2,1]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => [2,2,1,1]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => [2,2,2]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => [3,2,1]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => [4,2]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => [3,1,1,1]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => [3,2,1]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => [3,2,1]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => [3,3]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => [4,1,1]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => [4,2]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => [5,1]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => [6]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => [2,2,1,1,1]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => [4,1,1,1]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => [2,2,1,1,1]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => [2,2,1,1,1]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => [3,2,1,1]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => [3,2,1,1]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => [4,1,1,1]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => [5,1,1]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => [2,1,1,1,1,1]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => [2,2,1,1,1]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => [2,2,1,1,1]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => [3,2,1,1]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => [2,2,1,1,1]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => [2,2,2,1]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => [3,2,1,1]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => [4,2,1]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => [3,2,1,1]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => [3,2,1,1]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => [3,3,1]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => [4,1,1,1]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => [4,2,1]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => [5,1,1]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => [6,1]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => [2,2,1,1,1]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => [2,2,1,1,1]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => [3,2,1,1]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => [2,2,1,1,1]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => [2,2,2,1]
>>> Load all 239 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => [3,2,1,1]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => [4,2,1]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => [2,2,2,1]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => [2,2,2,1]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => [3,2,2]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => [3,2,1,1]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => [3,2,2]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => [4,2,1]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => [5,2]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => [3,2,1,1]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => [3,2,1,1]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => [3,3,1]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => [3,2,1,1]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => [3,2,2]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => [3,3,1]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => [4,3]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => [4,1,1,1]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => [4,2,1]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => [4,2,1]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => [4,3]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => [5,1,1]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => [5,2]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => [6,1]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => [7]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,1]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => [3,1,1,1,1,1]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}} => [2,1,1,1,1,1,1]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => [2,2,1,1,1,1]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => [3,1,1,1,1,1]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => [4,1,1,1,1]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => [2,2,1,1,1,1]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => [5,1,1,1]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}} => [2,2,1,1,1,1]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}} => [4,2,1,1]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => [3,1,1,1,1,1]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}} => [3,3,1,1]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => [4,2,1,1]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => [5,1,1,1]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => [6,1,1]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}} => [4,2,1,1]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => [2,2,2,1,1]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => [3,2,2,1]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => [3,2,2,1]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => [5,2,1]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => [3,1,1,1,1,1]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => [3,3,1,1]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => [3,2,2,1]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => [5,1,1,1]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => [5,2,1]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => [7,1]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => [4,2,1,1]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => [3,2,2,1]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => [3,2,2,1]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => [5,2,1]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => [3,2,2,1]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => [4,2,2]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}} => [3,2,1,1,1]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => [4,2,2]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => [5,2,1]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => [6,2]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => [3,2,1,1,1]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => [4,3,1]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => [5,3]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => [4,2,1,1]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => [4,2,2]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => [4,3,1]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => [4,4]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => [5,2,1]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => [5,3]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => [6,1,1]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => [6,2]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => [7,1]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => [8]
[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => [2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => [3,1,1,1,1,1,1]
[1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7},{8,9}} => [2,2,1,1,1,1,1]
[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => [7,1,1]
[1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7},{8,9}} => [2,2,1,1,1,1,1]
[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7},{8},{9}} => [2,2,1,1,1,1,1]
[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6,7},{8,9}} => [6,2,1]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => [8,1]
[2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => [2,2,1,1,1,1,1]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7,8},{9}} => [6,2,1]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9}} => [7,2]
[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => [3,1,1,1,1,1,1]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => [6,3]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9}} => [4,1,1,1,1,1]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => [5,4]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9}} => [5,1,1,1,1]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}} => [5,3,1]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => [5,4]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9}} => [6,1,1,1]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => [6,2,1]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => [6,3]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9}} => [7,1,1]
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => [7,2]
[8,1] => [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},{9}} => [8,1]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9}} => [9]
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => [9,1]
[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => [2,2,1,1,1,1,1,1]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8,9,10}} => [8,2]
[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [3,1,1,1,1,1,1,1]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9,10}} => [7,3]
[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [4,1,1,1,1,1,1]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9,10}} => [6,4]
[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => [5,1,1,1,1,1]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9,10}} => [5,5]
[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => [6,1,1,1,1]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => [6,4]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9},{10}} => [7,1,1,1]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}} => [7,2,1]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => [7,3]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7,8},{9},{10}} => [8,1,1]
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => [8,2]
[9,1] => [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},{10}} => [9,1]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10}} => [10]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => [10,1]
[10,1] => [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},{11}} => [10,1]
[1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => [2,1,1,1,1,1,1,1,1,1]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.