- FindStat

Identifier

Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00115: Set partitions —Kasraoui-Zeng⟶ Set partitions
Mp00164: Set partitions —Chen Deng Du Stanley Yan⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 196 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

Map

Chen Deng Du Stanley Yan

Description

A map that swaps the crossing number and the nesting number of a set partition.