Identifier
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00144: Perfect matchings —rotation⟶ Perfect matchings
Images
[1,0] => [(1,2)] => [(1,2)]
[1,0,1,0] => [(1,2),(3,4)] => [(1,4),(2,3)]
[1,1,0,0] => [(1,4),(2,3)] => [(1,2),(3,4)]
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [(1,6),(2,3),(4,5)]
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [(1,4),(2,3),(5,6)]
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [(1,6),(2,5),(3,4)]
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [(1,2),(3,4),(5,6)]
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [(1,2),(3,6),(4,5)]
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [(1,8),(2,3),(4,5),(6,7)]
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [(1,6),(2,3),(4,5),(7,8)]
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [(1,8),(2,3),(4,7),(5,6)]
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [(1,4),(2,3),(5,6),(7,8)]
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [(1,4),(2,3),(5,8),(6,7)]
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [(1,8),(2,5),(3,4),(6,7)]
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [(1,6),(2,5),(3,4),(7,8)]
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [(1,8),(2,7),(3,4),(5,6)]
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [(1,2),(3,4),(5,6),(7,8)]
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [(1,2),(3,4),(5,8),(6,7)]
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [(1,8),(2,7),(3,6),(4,5)]
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [(1,2),(3,6),(4,5),(7,8)]
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [(1,2),(3,8),(4,5),(6,7)]
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [(1,2),(3,8),(4,7),(5,6)]
[1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => [(1,10),(2,3),(4,5),(6,7),(8,9)]
[1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => [(1,8),(2,3),(4,5),(6,7),(9,10)]
[1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [(1,10),(2,3),(4,5),(6,9),(7,8)]
[1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => [(1,6),(2,3),(4,5),(7,8),(9,10)]
[1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => [(1,6),(2,3),(4,5),(7,10),(8,9)]
[1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [(1,10),(2,3),(4,7),(5,6),(8,9)]
[1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [(1,8),(2,3),(4,7),(5,6),(9,10)]
[1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => [(1,10),(2,3),(4,9),(5,6),(7,8)]
[1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => [(1,4),(2,3),(5,6),(7,8),(9,10)]
[1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => [(1,4),(2,3),(5,6),(7,10),(8,9)]
[1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [(1,10),(2,3),(4,9),(5,8),(6,7)]
[1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [(1,4),(2,3),(5,8),(6,7),(9,10)]
[1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [(1,4),(2,3),(5,10),(6,7),(8,9)]
[1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [(1,4),(2,3),(5,10),(6,9),(7,8)]
[1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [(1,10),(2,5),(3,4),(6,7),(8,9)]
[1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [(1,8),(2,5),(3,4),(6,7),(9,10)]
[1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => [(1,10),(2,5),(3,4),(6,9),(7,8)]
[1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => [(1,6),(2,5),(3,4),(7,8),(9,10)]
[1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [(1,6),(2,5),(3,4),(7,10),(8,9)]
[1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [(1,10),(2,7),(3,4),(5,6),(8,9)]
[1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [(1,8),(2,7),(3,4),(5,6),(9,10)]
[1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [(1,10),(2,9),(3,4),(5,6),(7,8)]
[1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [(1,2),(3,4),(5,6),(7,8),(9,10)]
[1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [(1,2),(3,4),(5,6),(7,10),(8,9)]
[1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [(1,10),(2,9),(3,4),(5,8),(6,7)]
[1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [(1,2),(3,4),(5,8),(6,7),(9,10)]
[1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [(1,2),(3,4),(5,10),(6,7),(8,9)]
[1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [(1,2),(3,4),(5,10),(6,9),(7,8)]
[1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [(1,10),(2,7),(3,6),(4,5),(8,9)]
[1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [(1,8),(2,7),(3,6),(4,5),(9,10)]
[1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [(1,10),(2,9),(3,6),(4,5),(7,8)]
[1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [(1,2),(3,6),(4,5),(7,8),(9,10)]
[1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [(1,2),(3,6),(4,5),(7,10),(8,9)]
[1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => [(1,10),(2,9),(3,8),(4,5),(6,7)]
[1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [(1,2),(3,8),(4,5),(6,7),(9,10)]
[1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [(1,2),(3,10),(4,5),(6,7),(8,9)]
[1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [(1,2),(3,10),(4,5),(6,9),(7,8)]
[1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [(1,10),(2,9),(3,8),(4,7),(5,6)]
[1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [(1,2),(3,8),(4,7),(5,6),(9,10)]
[1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [(1,2),(3,10),(4,7),(5,6),(8,9)]
[1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => [(1,2),(3,10),(4,9),(5,6),(7,8)]
[1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [(1,2),(3,10),(4,9),(5,8),(6,7)]
[1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]
[1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]
[1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]
[1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]
[1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]
[1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]
[1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]
[1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]
[1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]
[1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]
[1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]
[1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]
[1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]
[1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]
[1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]
[1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]
[1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]
[1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]
[1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]
[1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]
[1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]
[1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]
[1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]
[1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]
[1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]
[1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]
[1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]
[1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]
[1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]
[1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]
[1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]
[1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]
[1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]
[1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]
[1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]
[1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]
[1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]
>>> Load all 200 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)] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]
[1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]
[1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]
[1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]
[1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]
[1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]
[1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]
[1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]
[1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]
[1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]
[1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]
[1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]
[1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]
[1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]
[1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]
[1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]
[1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]
[1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]
[1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]
[1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]
[1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]
[1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]
[1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]
[1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]
[1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]
[1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]
[1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]
[1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
[1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]
[1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]
[1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]
[1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]
[1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]
[1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]
[1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]
[1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]
[1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]
[1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]
[1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]
[1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]
[1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]
[1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
[1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]
[1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]
[1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]
[1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]
[1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]
[1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]
[1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]
[1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]
[1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]
[1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]
[1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]
[1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]
[1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]
[1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
[1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
[1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]
[1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]
[1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]
[1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]
[1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]
[1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]
[1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]
[1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
[1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]
[1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]
[1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]
[1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]
[1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]
[1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]
[1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]
[1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]
[1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]
[1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
[1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]
[1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]
[1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]
[1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
[1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]
[1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]
[1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]
[1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]
[1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]
[1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]
[1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]
[1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]
[1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]
[1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
[1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]
[1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]
[1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]
[1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]
[1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]
[1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)] => [(1,16),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)] => [(1,18),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)] => [(1,20),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]
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
rotation
Description
The rotation of a perfect matching.
This returns the perfect matching obtained by relabelling $i$ to $i+1$ cyclically.