Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Images
=>
Cc0005;cc-rep-1Cc0009;cc-rep-2
[1]=>[1,0]=>{{1}} [1,1]=>[1,0,1,0]=>{{1},{2}} [2]=>[1,1,0,0]=>{{1,2}} [1,1,1]=>[1,0,1,0,1,0]=>{{1},{2},{3}} [1,2]=>[1,0,1,1,0,0]=>{{1},{2,3}} [2,1]=>[1,1,0,0,1,0]=>{{1,2},{3}} [3]=>[1,1,1,0,0,0]=>{{1,2,3}} [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}} [1,1,2]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}} [1,2,1]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}} [1,3]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}} [2,1,1]=>[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}} [2,2]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}} [3,1]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}} [4]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}} [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}} [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}} [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}} [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}} [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}} [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}} [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}} [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}} [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}} [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}} [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}} [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}} [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}} [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}} [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}} [5]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}} [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}} [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}} [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}} [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}} [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}} [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}} [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}} [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}} [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}} [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}} [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}} [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}} [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}} [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}} [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}} [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}} [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}} [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}} [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}} [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}} [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}} [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}} [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}} [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}} [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}} [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}} [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}} [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}} [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}} [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}} [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}} [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}} [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}} [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}} [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}} [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}} [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}} [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}} [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}} [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}} [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}} [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}} [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}} [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}} [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}} [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}} [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}} [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}} [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}} [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}} [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}} [2,2,1,2]=>[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]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}} [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}} [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}} [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}} [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}} [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}} [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}} [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}} [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}} [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}} [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}} [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}} [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}} [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}} [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}} [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}} [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}} [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}} [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}} [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}} [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}} [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}} [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}} [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}} [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}} [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}} [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}} [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}} [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}} [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}} [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}} [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}} [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}} [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}} [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3},{4,5,6},{7},{8}} [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}} [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}} [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}} [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7},{8}} [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}} [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5},{6,7},{8}} [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5},{6,7,8}} [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}} [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}} [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4},{5,6,7},{8}} [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}} [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}} [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4,5},{6},{7,8}} [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4,5},{6,7},{8}} [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}} [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5,6},{7},{8}} [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}} [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}} [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}} [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}} [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}} [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}} [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}} [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5,6},{7},{8}} [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4},{5,6},{7,8}} [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4},{5,6,7},{8}} [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}} [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}} [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4,5},{6},{7,8}} [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}} [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}} [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3},{4,5,6},{7},{8}} [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}} [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3},{4,5,6,7},{8}} [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}} [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}} [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6},{7,8}} [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5},{6,7},{8}} [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}} [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3,4},{5,6},{7},{8}} [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}} [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5,6,7},{8}} [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}} [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}} [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}} [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4,5},{6,7},{8}} [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}} [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}} [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}} [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}} [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}} [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}} [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7,8}} [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6,7},{8}} [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5},{6,7,8}} [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4},{5,6},{7},{8}} [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4},{5,6},{7,8}} [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4},{5,6,7},{8}} [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}} [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8}} [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5},{6},{7,8}} [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6,7},{8}} [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}} [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3},{4,5,6},{7},{8}} [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}} [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}} [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}} [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}} [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6},{7,8}} [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5},{6,7},{8}} [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}} [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7},{8}} [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}} [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4},{5,6,7},{8}} [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}} [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}} [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2},{3,4,5},{6},{7,8}} [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2},{3,4,5},{6,7},{8}} [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}} [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2},{3,4,5,6},{7},{8}} [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}} [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}} [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}} [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}} [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6},{7,8}} [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5},{6,7},{8}} [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}} [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4},{5,6},{7},{8}} [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}} [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4},{5,6,7},{8}} [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}} [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8}} [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2,3},{4,5},{6},{7,8}} [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}} [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5},{6,7,8}} [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}} [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}} [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}} [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}} [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}} [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6},{7,8}} [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}} [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3,4},{5},{6,7,8}} [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}} [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}} [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}} [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}} [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}} [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4,5},{6},{7,8}} [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}} [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}} [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}} [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}} [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}} [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}} [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}} [1,1,1,1,1,1,1,2]=>[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}} [1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}} [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}} [1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8},{9}} [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}} [1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7,8},{9}} [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9}} [1,1,1,1,2,1,1,1]=>[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}} [1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}} [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9}} [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}} [1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8,9}} [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9}} [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}} [1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4},{5,6,7,8,9}} [1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7,8},{9}} [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}} [1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}} [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8,9}} [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}} [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}} [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}} [2,1,1,1,1,1,2]=>[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}} [2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6},{7,8},{9}} [2,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6,7},{8},{9}} [2,1,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7},{8,9}} [2,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5,6},{7},{8},{9}} [2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8},{9}} [2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}} [2,7]=>[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}} [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}} [3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8,9}} [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}} [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]=>[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}} [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}} [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}} [7,2]=>[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}} [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}} [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}} [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}} [1,1,1,1,1,1,1,1,2]=>[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}} [1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9},{10}} [1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}} [1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9},{10}} [1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}} [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}} [1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}} [1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5,6},{7},{8},{9},{10}} [1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9,10}} [1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8},{9},{10}} [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9,10}} [1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7},{8},{9},{10}} [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9,10}} [1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8},{9},{10}} [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8,9},{10}} [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}} [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}} [2,1,1,1,1,1,1,2]=>[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}} [2,8]=>[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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}} [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}}
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.