Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00171: Set partitions —intertwining number to dual major index⟶ Set partitions
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00171: Set partitions —intertwining number to dual major index⟶ 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}}=>{{1,2,4,6},{3},{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}}=>{{1,3,5},{2},{4,6}}
[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}}=>{{1,2,4,6,8},{3},{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}}=>{{1,2,4,7},{3,8},{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}}=>{{1,2,5,8},{3,6},{4},{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}}=>{{1,2,5,7},{3},{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}}=>{{1,3,6,8},{2,4},{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}}=>{{1,3,5,8},{2},{4,6},{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}}=>{{1,3,5,7},{2},{4},{6,8}}
[1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,3,6},{2,7},{4},{5,8}}
[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}}=>{{1,4,7},{2,5},{3},{6,8}}
[1,1,1,0,1,0,0,0]=>[(1,8),(2,7),(3,4),(5,6)]=>{{1,8},{2,7},{3,4},{5,6}}=>{{1,4,6},{2},{3,7},{5,8}}
[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}}=>{{1,2,4,6,8,10},{3},{5},{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}}=>{{1,2,4,6,9},{3,10},{5},{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}}=>{{1,2,4,7,10},{3,8},{5},{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}}=>{{1,2,4,7,9},{3},{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}}=>{{1,2,4,8},{3,9},{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}}=>{{1,2,5,8,10},{3,6},{4},{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}}=>{{1,2,5,9},{3,6,10},{4},{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}}=>{{1,2,5,7,10},{3},{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}}=>{{1,2,5,7,9},{3},{4},{6,10},{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}}=>{{1,2,5,8},{3,9},{4},{6,10},{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}}=>{{1,2,6,10},{3,7},{4,8},{5},{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}}=>{{1,2,6,9},{3,7},{4},{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}}=>{{1,2,6,8},{3},{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}}=>{{1,3,6,8,10},{2,4},{5},{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}}=>{{1,3,6,9},{2,4,10},{5},{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}}=>{{1,3,7,10},{2,4,8},{5},{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}}=>{{1,3,7,9},{2,4},{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}}=>{{1,3,5,8,10},{2},{4,6},{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}}=>{{1,3,5,9},{2,10},{4,6},{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}}=>{{1,3,5,7,10},{2},{4},{6,8},{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}}=>{{1,3,5,7,9},{2},{4},{6},{8,10}}
[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}}=>{{1,3,5,8},{2,9},{4},{6},{7,10}}
[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}}=>{{1,3,6,10},{2,7},{4},{5,8},{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}}=>{{1,3,6,9},{2,7},{4},{5},{8,10}}
[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}}=>{{1,3,6,8},{2},{4,9},{5},{7,10}}
[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}}=>{{1,3,7},{2,8},{4,9},{5},{6,10}}
[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}}=>{{1,4,8,10},{2,5},{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}}=>{{1,4,7,10},{2,5},{3},{6,8},{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}}=>{{1,4,7,9},{2,5},{3},{6},{8,10}}
[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}}=>{{1,4,8},{2,5,9},{3},{6},{7,10}}
[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}}=>{{1,4,6,10},{2},{3,7},{5,8},{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}}=>{{1,4,6,9},{2},{3,7},{5},{8,10}}
[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}}=>{{1,4,6,8},{2},{3},{5,9},{7,10}}
[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}}=>{{1,4,7},{2,8},{3},{5,9},{6,10}}
[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}}=>{{1,5,9},{2,6},{3,7},{4},{8,10}}
[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}}=>{{1,5,8},{2,6},{3},{4,9},{7,10}}
[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}}=>{{1,5,7},{2},{3,8},{4,9},{6,10}}
[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}}=>{{1,2,4,6,8,10,12},{3},{5},{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}}=>{{1,2,4,6,8,11},{3,12},{5},{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}}=>{{1,2,4,6,9,12},{3,10},{5},{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}}=>{{1,2,4,6,9,11},{3},{5,12},{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}}=>{{1,2,4,6,10},{3,11},{5,12},{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}}=>{{1,2,4,7,10,12},{3,8},{5},{6},{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}}=>{{1,2,4,7,11},{3,8,12},{5},{6},{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}}=>{{1,2,4,7,9,12},{3},{5,10},{6},{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}}=>{{1,2,4,7,9,11},{3},{5},{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}}=>{{1,2,4,7,10},{3,11},{5},{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}}=>{{1,2,4,8,12},{3,9},{5,10},{6},{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}}=>{{1,2,4,8,11},{3,9},{5},{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}}=>{{1,2,4,8,10},{3},{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}}=>{{1,2,4,9},{3,10},{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}}=>{{1,2,5,8,10,12},{3,6},{4},{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}}=>{{1,2,5,8,11},{3,6,12},{4},{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}}=>{{1,2,5,9,12},{3,6,10},{4},{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}}=>{{1,2,5,9,11},{3,6},{4,12},{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}}=>{{1,2,5,10},{3,6,11},{4,12},{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}}=>{{1,2,5,7,10,12},{3},{4,8},{6},{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}}=>{{1,2,5,7,11},{3,12},{4,8},{6},{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}}=>{{1,2,5,7,9,12},{3},{4},{6,10},{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}}=>{{1,2,5,7,9,11},{3},{4},{6},{8,12},{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}}=>{{1,2,5,7,10},{3,11},{4},{6},{8,12},{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}}=>{{1,2,5,8,12},{3,9},{4},{6,10},{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}}=>{{1,2,5,8,11},{3,9},{4},{6},{7,12},{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}}=>{{1,2,5,8,10},{3},{4,11},{6},{7,12},{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}}=>{{1,2,5,9},{3,10},{4,11},{6},{7,12},{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}}=>{{1,2,6,10,12},{3,7},{4,8},{5},{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}}=>{{1,2,6,11},{3,7,12},{4,8},{5},{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}}=>{{1,2,6,9,12},{3,7},{4},{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}}=>{{1,2,6,9,11},{3,7},{4},{5},{8,12},{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}}=>{{1,2,6,10},{3,7,11},{4},{5},{8,12},{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}}=>{{1,2,6,8,12},{3},{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}}=>{{1,2,6,8,11},{3},{4,9},{5},{7,12},{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}}=>{{1,2,6,8,10},{3},{4},{5,11},{7,12},{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}}=>{{1,2,6,9},{3,10},{4},{5,11},{7,12},{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}}=>{{1,2,7,12},{3,8},{4,9},{5,10},{6},{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}}=>{{1,2,7,11},{3,8},{4,9},{5},{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}}=>{{1,2,7,10},{3,8},{4},{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}}=>{{1,2,7,9},{3},{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}}=>{{1,3,6,8,10,12},{2,4},{5},{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}}=>{{1,3,6,8,11},{2,4,12},{5},{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}}=>{{1,3,6,9,12},{2,4,10},{5},{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}}=>{{1,3,6,9,11},{2,4},{5,12},{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}}=>{{1,3,6,10},{2,4,11},{5,12},{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}}=>{{1,3,7,10,12},{2,4,8},{5},{6},{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}}=>{{1,3,7,11},{2,4,8,12},{5},{6},{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}}=>{{1,3,7,9,12},{2,4},{5,10},{6},{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}}=>{{1,3,7,9,11},{2,4},{5},{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}}=>{{1,3,7,10},{2,4,11},{5},{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}}=>{{1,3,8,12},{2,4,9},{5,10},{6},{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}}=>{{1,3,8,11},{2,4,9},{5},{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}}=>{{1,3,8,10},{2,4},{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}}=>{{1,3,5,8,10,12},{2},{4,6},{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}}=>{{1,3,5,8,11},{2,12},{4,6},{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}}=>{{1,3,5,9,12},{2,10},{4,6},{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}}=>{{1,3,5,9,11},{2},{4,6,12},{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}}=>{{1,3,5,10},{2,11},{4,6,12},{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}}=>{{1,3,5,7,10,12},{2},{4},{6,8},{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}}=>{{1,3,5,7,11},{2,12},{4},{6,8},{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}}=>{{1,3,5,7,9,12},{2},{4},{6},{8,10},{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}}=>{{1,3,5,7,9,11},{2},{4},{6},{8},{10,12}}
[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}}=>{{1,3,5,7,10},{2,11},{4},{6},{8},{9,12}}
[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}}=>{{1,3,5,8,12},{2,9},{4},{6},{7,10},{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}}=>{{1,3,5,8,11},{2,9},{4},{6},{7},{10,12}}
[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}}=>{{1,3,5,8,10},{2},{4,11},{6},{7},{9,12}}
[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}}=>{{1,3,5,9},{2,10},{4,11},{6},{7},{8,12}}
[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}}=>{{1,3,6,10,12},{2,7},{4},{5,8},{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}}=>{{1,3,6,11},{2,7,12},{4},{5,8},{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}}=>{{1,3,6,9,12},{2,7},{4},{5},{8,10},{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}}=>{{1,3,6,9,11},{2,7},{4},{5},{8},{10,12}}
[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}}=>{{1,3,6,10},{2,7,11},{4},{5},{8},{9,12}}
[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}}=>{{1,3,6,8,12},{2},{4,9},{5},{7,10},{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}}=>{{1,3,6,8,11},{2},{4,9},{5},{7},{10,12}}
[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}}=>{{1,3,6,8,10},{2},{4},{5,11},{7},{9,12}}
[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}}=>{{1,3,6,9},{2,10},{4},{5,11},{7},{8,12}}
[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}}=>{{1,3,7,12},{2,8},{4,9},{5},{6,10},{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}}=>{{1,3,7,11},{2,8},{4,9},{5},{6},{10,12}}
[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}}=>{{1,3,7,10},{2,8},{4},{5,11},{6},{9,12}}
[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}}=>{{1,3,7,9},{2},{4,10},{5,11},{6},{8,12}}
[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}}=>{{1,3,8},{2,9},{4,10},{5,11},{6},{7,12}}
[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}}=>{{1,4,8,10,12},{2,5},{3,6},{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}}=>{{1,4,8,11},{2,5,12},{3,6},{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}}=>{{1,4,9,12},{2,5,10},{3,6},{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}}=>{{1,4,9,11},{2,5},{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}}=>{{1,4,7,10,12},{2,5},{3},{6,8},{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}}=>{{1,4,7,11},{2,5,12},{3},{6,8},{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}}=>{{1,4,7,9,12},{2,5},{3},{6},{8,10},{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}}=>{{1,4,7,9,11},{2,5},{3},{6},{8},{10,12}}
[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}}=>{{1,4,7,10},{2,5,11},{3},{6},{8},{9,12}}
[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}}=>{{1,4,8,12},{2,5,9},{3},{6},{7,10},{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}}=>{{1,4,8,11},{2,5,9},{3},{6},{7},{10,12}}
[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}}=>{{1,4,8,10},{2,5},{3,11},{6},{7},{9,12}}
[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}}=>{{1,4,9},{2,5,10},{3,11},{6},{7},{8,12}}
[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}}=>{{1,4,6,10,12},{2},{3,7},{5,8},{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}}=>{{1,4,6,11},{2,12},{3,7},{5,8},{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}}=>{{1,4,6,9,12},{2},{3,7},{5},{8,10},{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}}=>{{1,4,6,9,11},{2},{3,7},{5},{8},{10,12}}
[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}}=>{{1,4,6,10},{2,11},{3,7},{5},{8},{9,12}}
[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}}=>{{1,4,6,8,12},{2},{3},{5,9},{7,10},{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}}=>{{1,4,6,8,11},{2},{3},{5,9},{7},{10,12}}
[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}}=>{{1,4,6,8,10},{2},{3},{5},{7,11},{9,12}}
[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}}=>{{1,4,6,9},{2,10},{3},{5},{7,11},{8,12}}
[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}}=>{{1,4,7,12},{2,8},{3},{5,9},{6,10},{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}}=>{{1,4,7,11},{2,8},{3},{5,9},{6},{10,12}}
[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}}=>{{1,4,7,10},{2,8},{3},{5},{6,11},{9,12}}
[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}}=>{{1,4,7,9},{2},{3,10},{5},{6,11},{8,12}}
[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}}=>{{1,4,8},{2,9},{3,10},{5},{6,11},{7,12}}
[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}}=>{{1,5,10,12},{2,6},{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}}=>{{1,5,9,12},{2,6},{3,7},{4},{8,10},{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}}=>{{1,5,9,11},{2,6},{3,7},{4},{8},{10,12}}
[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}}=>{{1,5,10},{2,6,11},{3,7},{4},{8},{9,12}}
[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}}=>{{1,5,8,12},{2,6},{3},{4,9},{7,10},{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}}=>{{1,5,8,11},{2,6},{3},{4,9},{7},{10,12}}
[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}}=>{{1,5,8,10},{2,6},{3},{4},{7,11},{9,12}}
[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}}=>{{1,5,9},{2,6,10},{3},{4},{7,11},{8,12}}
[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}}=>{{1,5,7,12},{2},{3,8},{4,9},{6,10},{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}}=>{{1,5,7,11},{2},{3,8},{4,9},{6},{10,12}}
[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}}=>{{1,5,7,10},{2},{3,8},{4},{6,11},{9,12}}
[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}}=>{{1,5,7,9},{2},{3},{4,10},{6,11},{8,12}}
[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}}=>{{1,5,8},{2,9},{3},{4,10},{6,11},{7,12}}
[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}}=>{{1,6,11},{2,7},{3,8},{4,9},{5},{10,12}}
[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}}=>{{1,6,10},{2,7},{3,8},{4},{5,11},{9,12}}
[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}}=>{{1,6,9},{2,7},{3},{4,10},{5,11},{8,12}}
[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}}=>{{1,6,8},{2},{3,9},{4,10},{5,11},{7,12}}
[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
intertwining number to dual major index
searching the database
Sorry, this map was not found in the database.