Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00116: Perfect matchings —Kasraoui-Zeng⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00116: Perfect matchings —Kasraoui-Zeng⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Images
[1,0] => [(1,2)] => [(1,2)] => [2,1]
[1,0,1,0] => [(1,2),(3,4)] => [(1,2),(3,4)] => [2,1,4,3]
[1,1,0,0] => [(1,4),(2,3)] => [(1,3),(2,4)] => [3,4,1,2]
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5]
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [(1,2),(3,5),(4,6)] => [2,1,5,6,3,4]
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [(1,3),(2,4),(5,6)] => [3,4,1,2,6,5]
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [(1,3),(2,5),(4,6)] => [3,5,1,6,2,4]
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [(1,4),(2,5),(3,6)] => [4,5,6,1,2,3]
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6]
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7]
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6]
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5]
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7]
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6]
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7]
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6]
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5]
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7]
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6]
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5]
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4]
[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)] => [2,1,4,3,6,5,8,7,10,9]
[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),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8]
[1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9]
[1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => [(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8]
[1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => [(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7]
[1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9]
[1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8]
[1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => [(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9]
[1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => [(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8]
[1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => [(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7]
[1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9]
[1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8]
[1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7]
[1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6]
[1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9]
[1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8]
[1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => [(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9]
[1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => [(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8]
[1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7]
[1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9]
[1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8]
[1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9]
[1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8]
[1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7]
[1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9]
[1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8]
[1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7]
[1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6]
[1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9]
[1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8]
[1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9]
[1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8]
[1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7]
[1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => [(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9]
[1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8]
[1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7]
[1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6]
[1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9]
[1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8]
[1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7]
[1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => [(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6]
[1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5]
[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)] => [2,1,4,3,6,5,8,7,10,9,12,11]
[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),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10]
[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),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11]
[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),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10]
[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),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9]
[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),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11]
[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),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10]
[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),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11]
[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),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10]
[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),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9]
[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),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11]
[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),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10]
[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),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9]
[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),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8]
[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),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11]
[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),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10]
[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),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11]
[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),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10]
[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),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9]
[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),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11]
[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),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10]
[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),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11]
[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),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10]
[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),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9]
[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),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11]
[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),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10]
[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),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9]
[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),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8]
[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),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11]
[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),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10]
[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),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11]
[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),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10]
[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),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9]
[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),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11]
[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),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10]
[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),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9]
[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),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8]
>>> Load all 200 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
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution for perfect matchings.
This yields the perfect matching with the number of nestings and crossings exchanged.
This yields the perfect matching with the number of nestings and crossings exchanged.
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.
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