Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00216: Set partitions —inverse Wachs-White⟶ Set partitions
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00216: Set partitions —inverse Wachs-White⟶ Set partitions
Images
[1,0] => [(1,2)] => {{1,2}} => {{1,2}}
[1,0,1,0] => [(1,2),(3,4)] => {{1,2},{3,4}} => {{1,2},{3,4}}
[1,1,0,0] => [(1,4),(2,3)] => {{1,4},{2,3}} => {{1,4},{2,3}}
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}}
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}}
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}}
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}}
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}}
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => {{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}}
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}}
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => {{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}}
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => {{1,2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7,8}}
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => {{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}}
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => {{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}}
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => {{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}}
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => {{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}}
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => {{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}}
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => {{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}}
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => {{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}}
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => {{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}}
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => {{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}}
[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}} => {{1,2},{3,4},{5,6},{7,8},{9,10}}
[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}} => {{1,4},{2,3},{5,6},{7,8},{9,10}}
[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}} => {{1,2},{3,6},{4,5},{7,8},{9,10}}
[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}} => {{1,6},{2,3},{4,5},{7,8},{9,10}}
[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}} => {{1,6},{2,5},{3,4},{7,8},{9,10}}
[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}} => {{1,2},{3,4},{5,8},{6,7},{9,10}}
[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}} => {{1,4},{2,3},{5,8},{6,7},{9,10}}
[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}} => {{1,2},{3,8},{4,5},{6,7},{9,10}}
[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}} => {{1,8},{2,3},{4,5},{6,7},{9,10}}
[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}} => {{1,8},{2,5},{3,4},{6,7},{9,10}}
[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}} => {{1,2},{3,8},{4,7},{5,6},{9,10}}
[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}} => {{1,8},{2,3},{4,7},{5,6},{9,10}}
[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}} => {{1,8},{2,7},{3,4},{5,6},{9,10}}
[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}} => {{1,8},{2,7},{3,6},{4,5},{9,10}}
[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}} => {{1,2},{3,4},{5,6},{7,10},{8,9}}
[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}} => {{1,4},{2,3},{5,6},{7,10},{8,9}}
[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}} => {{1,2},{3,6},{4,5},{7,10},{8,9}}
[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}} => {{1,6},{2,3},{4,5},{7,10},{8,9}}
[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}} => {{1,6},{2,5},{3,4},{7,10},{8,9}}
[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}} => {{1,2},{3,4},{5,10},{6,7},{8,9}}
[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}} => {{1,4},{2,3},{5,10},{6,7},{8,9}}
[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}} => {{1,2},{3,10},{4,5},{6,7},{8,9}}
[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}} => {{1,10},{2,3},{4,5},{6,7},{8,9}}
[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}} => {{1,10},{2,5},{3,4},{6,7},{8,9}}
[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}} => {{1,2},{3,10},{4,7},{5,6},{8,9}}
[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}} => {{1,10},{2,3},{4,7},{5,6},{8,9}}
[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}} => {{1,10},{2,7},{3,4},{5,6},{8,9}}
[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}} => {{1,10},{2,7},{3,6},{4,5},{8,9}}
[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}} => {{1,2},{3,4},{5,10},{6,9},{7,8}}
[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}} => {{1,4},{2,3},{5,10},{6,9},{7,8}}
[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}} => {{1,2},{3,10},{4,5},{6,9},{7,8}}
[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}} => {{1,10},{2,3},{4,5},{6,9},{7,8}}
[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}} => {{1,10},{2,5},{3,4},{6,9},{7,8}}
[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}} => {{1,2},{3,10},{4,9},{5,6},{7,8}}
[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}} => {{1,10},{2,3},{4,9},{5,6},{7,8}}
[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}} => {{1,10},{2,9},{3,4},{5,6},{7,8}}
[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}} => {{1,10},{2,9},{3,6},{4,5},{7,8}}
[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}} => {{1,2},{3,10},{4,9},{5,8},{6,7}}
[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}} => {{1,10},{2,3},{4,9},{5,8},{6,7}}
[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}} => {{1,10},{2,9},{3,4},{5,8},{6,7}}
[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}} => {{1,10},{2,9},{3,8},{4,5},{6,7}}
[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}} => {{1,10},{2,9},{3,8},{4,7},{5,6}}
[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}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[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}} => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}
[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}} => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}
[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}} => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}
[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}} => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}
[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}} => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}
[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}} => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}
[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}} => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}
[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}} => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}
[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}} => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}
[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}} => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}
[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}} => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}
[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}} => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}
[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}} => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}
[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}} => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}
[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}} => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}
[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}} => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}
[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}} => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}
[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}} => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}
[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}} => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}
[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}} => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}
[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}} => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}
[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}} => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}
[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}} => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}
[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}} => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}
[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}} => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}
[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}} => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}
[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}} => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}
[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}} => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}
[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}} => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}
[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}} => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}
[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}} => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}
[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}} => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}
[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}} => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}
[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}} => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}
[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}} => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}
[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}} => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}
>>> Load all 196 entries. <<<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.
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.
Map
inverse Wachs-White
Description
The inverse of a transformation of set partitions due to Wachs and White.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma^{-1}$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection $\gamma^{-1}$.
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with $(i,j)$ to the cell in the $i$-th column from the right and the $j$-th row from the top.
searching the database
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