Identifier
Mp00142: Dyck paths promotionDyck paths
Mp00146: Dyck paths to tunnel matchingPerfect matchings
Mp00092: Perfect matchings to set partition Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0012;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[1,0]=>[(1,2)]=>{{1,2}} [1,0,1,0]=>[1,1,0,0]=>[(1,4),(2,3)]=>{{1,4},{2,3}} [1,1,0,0]=>[1,0,1,0]=>[(1,2),(3,4)]=>{{1,2},{3,4}} [1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[(1,6),(2,3),(4,5)]=>{{1,6},{2,3},{4,5}} [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[(1,4),(2,3),(5,6)]=>{{1,4},{2,3},{5,6}} [1,1,0,0,1,0]=>[1,1,1,0,0,0]=>[(1,6),(2,5),(3,4)]=>{{1,6},{2,5},{3,4}} [1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[(1,2),(3,4),(5,6)]=>{{1,2},{3,4},{5,6}} [1,1,1,0,0,0]=>[1,0,1,1,0,0]=>[(1,2),(3,6),(4,5)]=>{{1,2},{3,6},{4,5}} [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[(1,8),(2,3),(4,5),(6,7)]=>{{1,8},{2,3},{4,5},{6,7}} [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,8)]=>{{1,6},{2,3},{4,5},{7,8}} [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>{{1,8},{2,3},{4,7},{5,6}} [1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8)]=>{{1,4},{2,3},{5,6},{7,8}} [1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7)]=>{{1,4},{2,3},{5,8},{6,7}} [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0]=>[(1,8),(2,5),(3,4),(6,7)]=>{{1,8},{2,5},{3,4},{6,7}} [1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,8)]=>{{1,6},{2,5},{3,4},{7,8}} [1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>[(1,8),(2,7),(3,4),(5,6)]=>{{1,8},{2,7},{3,4},{5,6}} [1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8)]=>{{1,2},{3,4},{5,6},{7,8}} [1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7)]=>{{1,2},{3,4},{5,8},{6,7}} [1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0]=>[(1,8),(2,7),(3,6),(4,5)]=>{{1,8},{2,7},{3,6},{4,5}} [1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,8)]=>{{1,2},{3,6},{4,5},{7,8}} [1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>[(1,2),(3,8),(4,5),(6,7)]=>{{1,2},{3,8},{4,5},{6,7}} [1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0]=>[(1,2),(3,8),(4,7),(5,6)]=>{{1,2},{3,8},{4,7},{5,6}} [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>{{1,10},{2,3},{4,5},{6,7},{8,9}} [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>{{1,8},{2,3},{4,5},{6,7},{9,10}} [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>{{1,10},{2,3},{4,5},{6,9},{7,8}} [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>{{1,6},{2,3},{4,5},{7,8},{9,10}} [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>{{1,6},{2,3},{4,5},{7,10},{8,9}} [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>{{1,10},{2,3},{4,7},{5,6},{8,9}} [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>{{1,8},{2,3},{4,7},{5,6},{9,10}} [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>{{1,10},{2,3},{4,9},{5,6},{7,8}} [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>{{1,4},{2,3},{5,6},{7,8},{9,10}} [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>{{1,4},{2,3},{5,6},{7,10},{8,9}} [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>{{1,10},{2,3},{4,9},{5,8},{6,7}} [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>{{1,4},{2,3},{5,8},{6,7},{9,10}} [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>{{1,4},{2,3},{5,10},{6,7},{8,9}} [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>{{1,4},{2,3},{5,10},{6,9},{7,8}} [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>{{1,10},{2,5},{3,4},{6,7},{8,9}} [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>{{1,8},{2,5},{3,4},{6,7},{9,10}} [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>{{1,10},{2,5},{3,4},{6,9},{7,8}} [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>{{1,6},{2,5},{3,4},{7,8},{9,10}} [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>{{1,6},{2,5},{3,4},{7,10},{8,9}} [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>{{1,10},{2,7},{3,4},{5,6},{8,9}} [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>{{1,8},{2,7},{3,4},{5,6},{9,10}} [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>{{1,10},{2,9},{3,4},{5,6},{7,8}} [1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>{{1,2},{3,4},{5,6},{7,8},{9,10}} [1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>{{1,2},{3,4},{5,6},{7,10},{8,9}} [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>{{1,10},{2,9},{3,4},{5,8},{6,7}} [1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>{{1,2},{3,4},{5,8},{6,7},{9,10}} [1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>{{1,2},{3,4},{5,10},{6,7},{8,9}} [1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>{{1,2},{3,4},{5,10},{6,9},{7,8}} [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>{{1,10},{2,7},{3,6},{4,5},{8,9}} [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>{{1,8},{2,7},{3,6},{4,5},{9,10}} [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>{{1,10},{2,9},{3,6},{4,5},{7,8}} [1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>{{1,2},{3,6},{4,5},{7,8},{9,10}} [1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>{{1,2},{3,6},{4,5},{7,10},{8,9}} [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>{{1,10},{2,9},{3,8},{4,5},{6,7}} [1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>{{1,2},{3,8},{4,5},{6,7},{9,10}} [1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>{{1,2},{3,10},{4,5},{6,7},{8,9}} [1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>{{1,2},{3,10},{4,5},{6,9},{7,8}} [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>{{1,10},{2,9},{3,8},{4,7},{5,6}} [1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>{{1,2},{3,8},{4,7},{5,6},{9,10}} [1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>{{1,2},{3,10},{4,7},{5,6},{8,9}} [1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>{{1,2},{3,10},{4,9},{5,6},{7,8}} [1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>{{1,2},{3,10},{4,9},{5,8},{6,7}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9),(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]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>{{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>{{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>{{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>{{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>{{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>{{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>{{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>{{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>{{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>{{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>{{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>{{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>{{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>{{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>{{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>{{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>{{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>{{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>{{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>{{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>{{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>{{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>{{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>{{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>{{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>{{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>{{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>{{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>{{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>{{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>{{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>{{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>{{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>{{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>{{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Sch├╝tzenberger's promotion. For definitions and details, see [1] and the references therein.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
to set partition
Description
Return the set partition corresponding to the perfect matching.