Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Images
[1,0] => [(1,2)] => [2,1] => {{1,2}}
[1,0,1,0] => [(1,2),(3,4)] => [2,1,4,3] => {{1,2},{3,4}}
[1,1,0,0] => [(1,4),(2,3)] => [3,4,2,1] => {{1,3},{2,4}}
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => {{1,2},{3,5},{4,6}}
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => {{1,3},{2,4},{5,6}}
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => {{1,3},{2,5},{4,6}}
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => {{1,4},{2,5},{3,6}}
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => {{1,2},{3,4},{5,7},{6,8}}
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => {{1,2},{3,5},{4,6},{7,8}}
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => {{1,2},{3,5},{4,7},{6,8}}
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => {{1,2},{3,6},{4,7},{5,8}}
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => {{1,3},{2,4},{5,7},{6,8}}
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => {{1,3},{2,5},{4,6},{7,8}}
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => {{1,3},{2,5},{4,7},{6,8}}
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => {{1,3},{2,6},{4,7},{5,8}}
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => {{1,4},{2,5},{3,6},{7,8}}
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => {{1,4},{2,5},{3,7},{6,8}}
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => {{1,4},{2,6},{3,7},{5,8}}
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => {{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)] => [2,1,4,3,6,5,8,7,10,9] => {{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)] => [2,1,4,3,6,5,9,10,8,7] => {{1,2},{3,4},{5,6},{7,9},{8,10}}
[1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,7,8,6,5,10,9] => {{1,2},{3,4},{5,7},{6,8},{9,10}}
[1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,7,9,6,10,8,5] => {{1,2},{3,4},{5,7},{6,9},{8,10}}
[1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,8,9,10,7,6,5] => {{1,2},{3,4},{5,8},{6,9},{7,10}}
[1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => {{1,2},{3,5},{4,6},{7,8},{9,10}}
[1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,5,6,4,3,9,10,8,7] => {{1,2},{3,5},{4,6},{7,9},{8,10}}
[1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,5,7,4,8,6,3,10,9] => {{1,2},{3,5},{4,7},{6,8},{9,10}}
[1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,5,7,4,9,6,10,8,3] => {{1,2},{3,5},{4,7},{6,9},{8,10}}
[1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,5,8,4,9,10,7,6,3] => {{1,2},{3,5},{4,8},{6,9},{7,10}}
[1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,6,7,8,5,4,3,10,9] => {{1,2},{3,6},{4,7},{5,8},{9,10}}
[1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,6,7,9,5,4,10,8,3] => {{1,2},{3,6},{4,7},{5,9},{8,10}}
[1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,6,8,9,5,10,7,4,3] => {{1,2},{3,6},{4,8},{5,9},{7,10}}
[1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,7,8,9,10,6,5,4,3] => {{1,2},{3,7},{4,8},{5,9},{6,10}}
[1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => {{1,3},{2,4},{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)] => [3,4,2,1,6,5,9,10,8,7] => {{1,3},{2,4},{5,6},{7,9},{8,10}}
[1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => [3,4,2,1,7,8,6,5,10,9] => {{1,3},{2,4},{5,7},{6,8},{9,10}}
[1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => [3,4,2,1,7,9,6,10,8,5] => {{1,3},{2,4},{5,7},{6,9},{8,10}}
[1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [3,4,2,1,8,9,10,7,6,5] => {{1,3},{2,4},{5,8},{6,9},{7,10}}
[1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [3,5,2,6,4,1,8,7,10,9] => {{1,3},{2,5},{4,6},{7,8},{9,10}}
[1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [3,5,2,6,4,1,9,10,8,7] => {{1,3},{2,5},{4,6},{7,9},{8,10}}
[1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [3,5,2,7,4,8,6,1,10,9] => {{1,3},{2,5},{4,7},{6,8},{9,10}}
[1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => {{1,3},{2,5},{4,7},{6,9},{8,10}}
[1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [3,5,2,8,4,9,10,7,6,1] => {{1,3},{2,5},{4,8},{6,9},{7,10}}
[1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [3,6,2,7,8,5,4,1,10,9] => {{1,3},{2,6},{4,7},{5,8},{9,10}}
[1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [3,6,2,7,9,5,4,10,8,1] => {{1,3},{2,6},{4,7},{5,9},{8,10}}
[1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [3,6,2,8,9,5,10,7,4,1] => {{1,3},{2,6},{4,8},{5,9},{7,10}}
[1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [3,7,2,8,9,10,6,5,4,1] => {{1,3},{2,7},{4,8},{5,9},{6,10}}
[1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [4,5,6,3,2,1,8,7,10,9] => {{1,4},{2,5},{3,6},{7,8},{9,10}}
[1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [4,5,6,3,2,1,9,10,8,7] => {{1,4},{2,5},{3,6},{7,9},{8,10}}
[1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [4,5,7,3,2,8,6,1,10,9] => {{1,4},{2,5},{3,7},{6,8},{9,10}}
[1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [4,5,7,3,2,9,6,10,8,1] => {{1,4},{2,5},{3,7},{6,9},{8,10}}
[1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [4,5,8,3,2,9,10,7,6,1] => {{1,4},{2,5},{3,8},{6,9},{7,10}}
[1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => [4,6,7,3,8,5,2,1,10,9] => {{1,4},{2,6},{3,7},{5,8},{9,10}}
[1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [4,6,7,3,9,5,2,10,8,1] => {{1,4},{2,6},{3,7},{5,9},{8,10}}
[1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [4,6,8,3,9,5,10,7,2,1] => {{1,4},{2,6},{3,8},{5,9},{7,10}}
[1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [4,7,8,3,9,10,6,5,2,1] => {{1,4},{2,7},{3,8},{5,9},{6,10}}
[1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [5,6,7,8,4,3,2,1,10,9] => {{1,5},{2,6},{3,7},{4,8},{9,10}}
[1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [5,6,7,9,4,3,2,10,8,1] => {{1,5},{2,6},{3,7},{4,9},{8,10}}
[1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [5,6,8,9,4,3,10,7,2,1] => {{1,5},{2,6},{3,8},{4,9},{7,10}}
[1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => [5,7,8,9,4,10,6,3,2,1] => {{1,5},{2,7},{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)] => [6,7,8,9,10,5,4,3,2,1] => {{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)] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{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)] => [2,1,4,3,6,5,8,7,11,12,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,11},{10,12}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,9,10,8,7,12,11] => {{1,2},{3,4},{5,6},{7,9},{8,10},{11,12}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,9,11,8,12,10,7] => {{1,2},{3,4},{5,6},{7,9},{8,11},{10,12}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,10,11,12,9,8,7] => {{1,2},{3,4},{5,6},{7,10},{8,11},{9,12}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,7,8,6,5,10,9,12,11] => {{1,2},{3,4},{5,7},{6,8},{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)] => [2,1,4,3,7,8,6,5,11,12,10,9] => {{1,2},{3,4},{5,7},{6,8},{9,11},{10,12}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,7,9,6,10,8,5,12,11] => {{1,2},{3,4},{5,7},{6,9},{8,10},{11,12}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,7,9,6,11,8,12,10,5] => {{1,2},{3,4},{5,7},{6,9},{8,11},{10,12}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,7,10,6,11,12,9,8,5] => {{1,2},{3,4},{5,7},{6,10},{8,11},{9,12}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,8,9,10,7,6,5,12,11] => {{1,2},{3,4},{5,8},{6,9},{7,10},{11,12}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,8,9,11,7,6,12,10,5] => {{1,2},{3,4},{5,8},{6,9},{7,11},{10,12}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,8,10,11,7,12,9,6,5] => {{1,2},{3,4},{5,8},{6,10},{7,11},{9,12}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,9,10,11,12,8,7,6,5] => {{1,2},{3,4},{5,9},{6,10},{7,11},{8,12}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,5,6,4,3,8,7,10,9,12,11] => {{1,2},{3,5},{4,6},{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)] => [2,1,5,6,4,3,8,7,11,12,10,9] => {{1,2},{3,5},{4,6},{7,8},{9,11},{10,12}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,5,6,4,3,9,10,8,7,12,11] => {{1,2},{3,5},{4,6},{7,9},{8,10},{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)] => [2,1,5,6,4,3,9,11,8,12,10,7] => {{1,2},{3,5},{4,6},{7,9},{8,11},{10,12}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,5,6,4,3,10,11,12,9,8,7] => {{1,2},{3,5},{4,6},{7,10},{8,11},{9,12}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,5,7,4,8,6,3,10,9,12,11] => {{1,2},{3,5},{4,7},{6,8},{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)] => [2,1,5,7,4,8,6,3,11,12,10,9] => {{1,2},{3,5},{4,7},{6,8},{9,11},{10,12}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,5,7,4,9,6,10,8,3,12,11] => {{1,2},{3,5},{4,7},{6,9},{8,10},{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)] => [2,1,5,7,4,9,6,11,8,12,10,3] => {{1,2},{3,5},{4,7},{6,9},{8,11},{10,12}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,5,7,4,10,6,11,12,9,8,3] => {{1,2},{3,5},{4,7},{6,10},{8,11},{9,12}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,5,8,4,9,10,7,6,3,12,11] => {{1,2},{3,5},{4,8},{6,9},{7,10},{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)] => [2,1,5,8,4,9,11,7,6,12,10,3] => {{1,2},{3,5},{4,8},{6,9},{7,11},{10,12}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,5,8,4,10,11,7,12,9,6,3] => {{1,2},{3,5},{4,8},{6,10},{7,11},{9,12}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,5,9,4,10,11,12,8,7,6,3] => {{1,2},{3,5},{4,9},{6,10},{7,11},{8,12}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,6,7,8,5,4,3,10,9,12,11] => {{1,2},{3,6},{4,7},{5,8},{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)] => [2,1,6,7,8,5,4,3,11,12,10,9] => {{1,2},{3,6},{4,7},{5,8},{9,11},{10,12}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,6,7,9,5,4,10,8,3,12,11] => {{1,2},{3,6},{4,7},{5,9},{8,10},{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)] => [2,1,6,7,9,5,4,11,8,12,10,3] => {{1,2},{3,6},{4,7},{5,9},{8,11},{10,12}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,6,7,10,5,4,11,12,9,8,3] => {{1,2},{3,6},{4,7},{5,10},{8,11},{9,12}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,6,8,9,5,10,7,4,3,12,11] => {{1,2},{3,6},{4,8},{5,9},{7,10},{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)] => [2,1,6,8,9,5,11,7,4,12,10,3] => {{1,2},{3,6},{4,8},{5,9},{7,11},{10,12}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,6,8,10,5,11,7,12,9,4,3] => {{1,2},{3,6},{4,8},{5,10},{7,11},{9,12}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,6,9,10,5,11,12,8,7,4,3] => {{1,2},{3,6},{4,9},{5,10},{7,11},{8,12}}
>>> Load all 196 entries. <<<Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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