Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00219: Set partitions —inverse Yip⟶ Set partitions
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00219: Set partitions —inverse Yip⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0012;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[(1,2)]=>{{1,2}}=>{{1,2}}
[1,0,1,0]=>[(1,2),(3,4)]=>{{1,2},{3,4}}=>{{1,2,4},{3}}
[1,1,0,0]=>[(1,4),(2,3)]=>{{1,4},{2,3}}=>{{1,3},{2,4}}
[1,0,1,0,1,0]=>[(1,2),(3,4),(5,6)]=>{{1,2},{3,4},{5,6}}=>{{1,2,4},{3,6},{5}}
[1,0,1,1,0,0]=>[(1,2),(3,6),(4,5)]=>{{1,2},{3,6},{4,5}}=>{{1,2,5},{3,6},{4}}
[1,1,0,0,1,0]=>[(1,4),(2,3),(5,6)]=>{{1,4},{2,3},{5,6}}=>{{1,3,6},{2,4},{5}}
[1,1,0,1,0,0]=>[(1,6),(2,3),(4,5)]=>{{1,6},{2,3},{4,5}}=>{{1,3,6},{2,5},{4}}
[1,1,1,0,0,0]=>[(1,6),(2,5),(3,4)]=>{{1,6},{2,5},{3,4}}=>{{1,4},{2,5},{3,6}}
[1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8)]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,8},{3,6},{5},{7}}
[1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7)]=>{{1,2},{3,4},{5,8},{6,7}}=>{{1,2,4,8},{3,7},{5},{6}}
[1,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,8)]=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,2,5},{3,6},{4,8},{7}}
[1,0,1,1,0,1,0,0]=>[(1,2),(3,8),(4,5),(6,7)]=>{{1,2},{3,8},{4,5},{6,7}}=>{{1,2,5},{3,7},{4,8},{6}}
[1,0,1,1,1,0,0,0]=>[(1,2),(3,8),(4,7),(5,6)]=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,2,6},{3,7},{4,8},{5}}
[1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8)]=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,3,6},{2,4,8},{5},{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}}=>{{1,3,7},{2,4,8},{5},{6}}
[1,1,0,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,8)]=>{{1,6},{2,3},{4,5},{7,8}}=>{{1,3,6},{2,5},{4,8},{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}}=>{{1,3,7},{2,5},{4,8},{6}}
[1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,3,7},{2,6},{4,8},{5}}
[1,1,1,0,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,8)]=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,4,8},{2,5},{3,6},{7}}
[1,1,1,0,0,1,0,0]=>[(1,8),(2,5),(3,4),(6,7)]=>{{1,8},{2,5},{3,4},{6,7}}=>{{1,4,8},{2,5},{3,7},{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}}=>{{1,4,8},{2,6},{3,7},{5}}
[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}}
[1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,8},{3,6},{5,10},{7},{9}}
[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}}=>{{1,2,4,9},{3,6},{5,10},{7},{8}}
[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}}=>{{1,2,4,8},{3,7},{5,10},{6},{9}}
[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}}=>{{1,2,4,9},{3,7},{5,10},{6},{8}}
[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}}=>{{1,2,4,9},{3,8},{5,10},{6},{7}}
[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}}=>{{1,2,5,10},{3,6},{4,8},{7},{9}}
[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}}=>{{1,2,5,10},{3,6},{4,9},{7},{8}}
[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}}=>{{1,2,5,10},{3,7},{4,8},{6},{9}}
[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}}=>{{1,2,5,10},{3,7},{4,9},{6},{8}}
[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}}=>{{1,2,5,10},{3,8},{4,9},{6},{7}}
[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}}=>{{1,2,6},{3,7},{4,8},{5,10},{9}}
[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}}=>{{1,2,6},{3,7},{4,9},{5,10},{8}}
[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}}=>{{1,2,6},{3,8},{4,9},{5,10},{7}}
[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}}=>{{1,2,7},{3,8},{4,9},{5,10},{6}}
[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}}=>{{1,3,6},{2,4,8},{5,10},{7},{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}}=>{{1,3,6},{2,4,9},{5,10},{7},{8}}
[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}}=>{{1,3,7},{2,4,8},{5,10},{6},{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}}=>{{1,3,7},{2,4,9},{5,10},{6},{8}}
[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}}=>{{1,3,8},{2,4,9},{5,10},{6},{7}}
[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}}=>{{1,3,6},{2,5,10},{4,8},{7},{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}}=>{{1,3,6},{2,5,10},{4,9},{7},{8}}
[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}}=>{{1,3,7},{2,5,10},{4,8},{6},{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}}=>{{1,3,7},{2,5,10},{4,9},{6},{8}}
[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}}=>{{1,3,8},{2,5,10},{4,9},{6},{7}}
[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}}=>{{1,3,7},{2,6},{4,8},{5,10},{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}}=>{{1,3,7},{2,6},{4,9},{5,10},{8}}
[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}}=>{{1,3,8},{2,6},{4,9},{5,10},{7}}
[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}}=>{{1,3,8},{2,7},{4,9},{5,10},{6}}
[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}}=>{{1,4,8},{2,5,10},{3,6},{7},{9}}
[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}}=>{{1,4,9},{2,5,10},{3,6},{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}}=>{{1,4,8},{2,5,10},{3,7},{6},{9}}
[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}}=>{{1,4,9},{2,5,10},{3,7},{6},{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}}=>{{1,4,9},{2,5,10},{3,8},{6},{7}}
[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}}=>{{1,4,8},{2,6},{3,7},{5,10},{9}}
[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}}=>{{1,4,9},{2,6},{3,7},{5,10},{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}}=>{{1,4,9},{2,6},{3,8},{5,10},{7}}
[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}}=>{{1,4,9},{2,7},{3,8},{5,10},{6}}
[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}}=>{{1,5,10},{2,6},{3,7},{4,8},{9}}
[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}}=>{{1,5,10},{2,6},{3,7},{4,9},{8}}
[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}}=>{{1,5,10},{2,6},{3,8},{4,9},{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}}=>{{1,5,10},{2,7},{3,8},{4,9},{6}}
[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}}
[1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,8},{3,6,12},{5,10},{7},{9},{11}}
[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}}=>{{1,2,4,8},{3,6,12},{5,11},{7},{9},{10}}
[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}}=>{{1,2,4,9},{3,6,12},{5,10},{7},{8},{11}}
[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}}=>{{1,2,4,9},{3,6,12},{5,11},{7},{8},{10}}
[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}}=>{{1,2,4,10},{3,6,12},{5,11},{7},{8},{9}}
[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}}=>{{1,2,4,8},{3,7},{5,10},{6,12},{9},{11}}
[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}}=>{{1,2,4,8},{3,7},{5,11},{6,12},{9},{10}}
[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}}=>{{1,2,4,9},{3,7},{5,10},{6,12},{8},{11}}
[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}}=>{{1,2,4,9},{3,7},{5,11},{6,12},{8},{10}}
[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}}=>{{1,2,4,10},{3,7},{5,11},{6,12},{8},{9}}
[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}}=>{{1,2,4,9},{3,8},{5,10},{6,12},{7},{11}}
[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}}=>{{1,2,4,9},{3,8},{5,11},{6,12},{7},{10}}
[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}}=>{{1,2,4,10},{3,8},{5,11},{6,12},{7},{9}}
[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}}=>{{1,2,4,10},{3,9},{5,11},{6,12},{7},{8}}
[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}}=>{{1,2,5,10},{3,6,12},{4,8},{7},{9},{11}}
[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}}=>{{1,2,5,11},{3,6,12},{4,8},{7},{9},{10}}
[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}}=>{{1,2,5,10},{3,6,12},{4,9},{7},{8},{11}}
[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}}=>{{1,2,5,11},{3,6,12},{4,9},{7},{8},{10}}
[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}}=>{{1,2,5,11},{3,6,12},{4,10},{7},{8},{9}}
[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}}=>{{1,2,5,10},{3,7},{4,8},{6,12},{9},{11}}
[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}}=>{{1,2,5,11},{3,7},{4,8},{6,12},{9},{10}}
[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}}=>{{1,2,5,10},{3,7},{4,9},{6,12},{8},{11}}
[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}}=>{{1,2,5,11},{3,7},{4,9},{6,12},{8},{10}}
[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}}=>{{1,2,5,11},{3,7},{4,10},{6,12},{8},{9}}
[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}}=>{{1,2,5,10},{3,8},{4,9},{6,12},{7},{11}}
[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}}=>{{1,2,5,11},{3,8},{4,9},{6,12},{7},{10}}
[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}}=>{{1,2,5,11},{3,8},{4,10},{6,12},{7},{9}}
[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}}=>{{1,2,5,11},{3,9},{4,10},{6,12},{7},{8}}
[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}}=>{{1,2,6,12},{3,7},{4,8},{5,10},{9},{11}}
[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}}=>{{1,2,6,12},{3,7},{4,8},{5,11},{9},{10}}
[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}}=>{{1,2,6,12},{3,7},{4,9},{5,10},{8},{11}}
[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}}=>{{1,2,6,12},{3,7},{4,9},{5,11},{8},{10}}
[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}}=>{{1,2,6,12},{3,7},{4,10},{5,11},{8},{9}}
[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}}=>{{1,2,6,12},{3,8},{4,9},{5,10},{7},{11}}
[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}}=>{{1,2,6,12},{3,8},{4,9},{5,11},{7},{10}}
[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}}=>{{1,2,6,12},{3,8},{4,10},{5,11},{7},{9}}
[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}}=>{{1,2,6,12},{3,9},{4,10},{5,11},{7},{8}}
[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}}=>{{1,2,7},{3,8},{4,9},{5,10},{6,12},{11}}
[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}}=>{{1,2,7},{3,8},{4,9},{5,11},{6,12},{10}}
[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}}=>{{1,2,7},{3,8},{4,10},{5,11},{6,12},{9}}
[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}}=>{{1,2,7},{3,9},{4,10},{5,11},{6,12},{8}}
[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}}=>{{1,2,8},{3,9},{4,10},{5,11},{6,12},{7}}
[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}}=>{{1,3,6,12},{2,4,8},{5,10},{7},{9},{11}}
[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}}=>{{1,3,6,12},{2,4,8},{5,11},{7},{9},{10}}
[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}}=>{{1,3,6,12},{2,4,9},{5,10},{7},{8},{11}}
[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}}=>{{1,3,6,12},{2,4,9},{5,11},{7},{8},{10}}
[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}}=>{{1,3,6,12},{2,4,10},{5,11},{7},{8},{9}}
[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}}=>{{1,3,7},{2,4,8},{5,10},{6,12},{9},{11}}
[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}}=>{{1,3,7},{2,4,8},{5,11},{6,12},{9},{10}}
[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}}=>{{1,3,7},{2,4,9},{5,10},{6,12},{8},{11}}
[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}}=>{{1,3,7},{2,4,9},{5,11},{6,12},{8},{10}}
[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}}=>{{1,3,7},{2,4,10},{5,11},{6,12},{8},{9}}
[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}}=>{{1,3,8},{2,4,9},{5,10},{6,12},{7},{11}}
[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}}=>{{1,3,8},{2,4,9},{5,11},{6,12},{7},{10}}
[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}}=>{{1,3,8},{2,4,10},{5,11},{6,12},{7},{9}}
[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}}=>{{1,3,9},{2,4,10},{5,11},{6,12},{7},{8}}
[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}}=>{{1,3,6,12},{2,5,10},{4,8},{7},{9},{11}}
[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}}=>{{1,3,6,12},{2,5,11},{4,8},{7},{9},{10}}
[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}}=>{{1,3,6,12},{2,5,10},{4,9},{7},{8},{11}}
[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}}=>{{1,3,6,12},{2,5,11},{4,9},{7},{8},{10}}
[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}}=>{{1,3,6,12},{2,5,11},{4,10},{7},{8},{9}}
[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}}=>{{1,3,7},{2,5,10},{4,8},{6,12},{9},{11}}
[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}}=>{{1,3,7},{2,5,11},{4,8},{6,12},{9},{10}}
[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}}=>{{1,3,7},{2,5,10},{4,9},{6,12},{8},{11}}
[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}}=>{{1,3,7},{2,5,11},{4,9},{6,12},{8},{10}}
[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}}=>{{1,3,7},{2,5,11},{4,10},{6,12},{8},{9}}
[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}}=>{{1,3,8},{2,5,10},{4,9},{6,12},{7},{11}}
[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}}=>{{1,3,8},{2,5,11},{4,9},{6,12},{7},{10}}
[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}}=>{{1,3,8},{2,5,11},{4,10},{6,12},{7},{9}}
[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}}=>{{1,3,9},{2,5,11},{4,10},{6,12},{7},{8}}
[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}}=>{{1,3,7},{2,6,12},{4,8},{5,10},{9},{11}}
[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}}=>{{1,3,7},{2,6,12},{4,8},{5,11},{9},{10}}
[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}}=>{{1,3,7},{2,6,12},{4,9},{5,10},{8},{11}}
[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}}=>{{1,3,7},{2,6,12},{4,9},{5,11},{8},{10}}
[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}}=>{{1,3,7},{2,6,12},{4,10},{5,11},{8},{9}}
[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}}=>{{1,3,8},{2,6,12},{4,9},{5,10},{7},{11}}
[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}}=>{{1,3,8},{2,6,12},{4,9},{5,11},{7},{10}}
[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}}=>{{1,3,8},{2,6,12},{4,10},{5,11},{7},{9}}
[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}}=>{{1,3,9},{2,6,12},{4,10},{5,11},{7},{8}}
[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}}=>{{1,3,8},{2,7},{4,9},{5,10},{6,12},{11}}
[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}}=>{{1,3,8},{2,7},{4,9},{5,11},{6,12},{10}}
[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}}=>{{1,3,8},{2,7},{4,10},{5,11},{6,12},{9}}
[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}}=>{{1,3,9},{2,7},{4,10},{5,11},{6,12},{8}}
[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}}=>{{1,3,9},{2,8},{4,10},{5,11},{6,12},{7}}
[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}}=>{{1,4,8},{2,5,10},{3,6,12},{7},{9},{11}}
[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}}=>{{1,4,8},{2,5,11},{3,6,12},{7},{9},{10}}
[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}}=>{{1,4,9},{2,5,10},{3,6,12},{7},{8},{11}}
[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}}=>{{1,4,9},{2,5,11},{3,6,12},{7},{8},{10}}
[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}}=>{{1,4,10},{2,5,11},{3,6,12},{7},{8},{9}}
[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}}=>{{1,4,8},{2,5,10},{3,7},{6,12},{9},{11}}
[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}}=>{{1,4,8},{2,5,11},{3,7},{6,12},{9},{10}}
[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}}=>{{1,4,9},{2,5,10},{3,7},{6,12},{8},{11}}
[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}}=>{{1,4,9},{2,5,11},{3,7},{6,12},{8},{10}}
[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}}=>{{1,4,10},{2,5,11},{3,7},{6,12},{8},{9}}
[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}}=>{{1,4,9},{2,5,10},{3,8},{6,12},{7},{11}}
[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}}=>{{1,4,9},{2,5,11},{3,8},{6,12},{7},{10}}
[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}}=>{{1,4,10},{2,5,11},{3,8},{6,12},{7},{9}}
[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}}=>{{1,4,10},{2,5,11},{3,9},{6,12},{7},{8}}
[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}}=>{{1,4,8},{2,6,12},{3,7},{5,10},{9},{11}}
[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}}=>{{1,4,8},{2,6,12},{3,7},{5,11},{9},{10}}
[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}}=>{{1,4,9},{2,6,12},{3,7},{5,10},{8},{11}}
[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}}=>{{1,4,9},{2,6,12},{3,7},{5,11},{8},{10}}
[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}}=>{{1,4,10},{2,6,12},{3,7},{5,11},{8},{9}}
[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}}=>{{1,4,9},{2,6,12},{3,8},{5,10},{7},{11}}
[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}}=>{{1,4,9},{2,6,12},{3,8},{5,11},{7},{10}}
[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}}=>{{1,4,10},{2,6,12},{3,8},{5,11},{7},{9}}
[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}}=>{{1,4,10},{2,6,12},{3,9},{5,11},{7},{8}}
[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}}=>{{1,4,9},{2,7},{3,8},{5,10},{6,12},{11}}
[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}}=>{{1,4,9},{2,7},{3,8},{5,11},{6,12},{10}}
[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}}=>{{1,4,10},{2,7},{3,8},{5,11},{6,12},{9}}
[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}}=>{{1,4,10},{2,7},{3,9},{5,11},{6,12},{8}}
[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}}=>{{1,4,10},{2,8},{3,9},{5,11},{6,12},{7}}
[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}}=>{{1,5,10},{2,6,12},{3,7},{4,8},{9},{11}}
[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}}=>{{1,5,11},{2,6,12},{3,7},{4,8},{9},{10}}
[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}}=>{{1,5,10},{2,6,12},{3,7},{4,9},{8},{11}}
[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}}=>{{1,5,11},{2,6,12},{3,7},{4,9},{8},{10}}
[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}}=>{{1,5,11},{2,6,12},{3,7},{4,10},{8},{9}}
[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}}=>{{1,5,10},{2,6,12},{3,8},{4,9},{7},{11}}
[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}}=>{{1,5,11},{2,6,12},{3,8},{4,9},{7},{10}}
[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}}=>{{1,5,11},{2,6,12},{3,8},{4,10},{7},{9}}
[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}}=>{{1,5,11},{2,6,12},{3,9},{4,10},{7},{8}}
[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}}=>{{1,5,10},{2,7},{3,8},{4,9},{6,12},{11}}
[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}}=>{{1,5,11},{2,7},{3,8},{4,9},{6,12},{10}}
[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}}=>{{1,5,11},{2,7},{3,8},{4,10},{6,12},{9}}
[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}}=>{{1,5,11},{2,7},{3,9},{4,10},{6,12},{8}}
[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}}=>{{1,5,11},{2,8},{3,9},{4,10},{6,12},{7}}
[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}}=>{{1,6,12},{2,7},{3,8},{4,9},{5,10},{11}}
[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}}=>{{1,6,12},{2,7},{3,8},{4,9},{5,11},{10}}
[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}}=>{{1,6,12},{2,7},{3,8},{4,10},{5,11},{9}}
[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}}=>{{1,6,12},{2,7},{3,9},{4,10},{5,11},{8}}
[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}}=>{{1,6,12},{2,8},{3,9},{4,10},{5,11},{7}}
[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}}
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 Yip
Description
The inverse of a transformation of set partitions due to Yip.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi^{-1}$.
Return the set partition of $\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Yip's bijection $\psi^{-1}$.
searching the database
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