Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Images
[1,0] => [(1,2)] => [2,1] => [2,1] => [2,1]
[1,0,1,0] => [(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3]
[1,1,0,0] => [(1,4),(2,3)] => [3,4,2,1] => [4,3,1,2] => [3,4,2,1]
[1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => [2,1,5,6,4,3]
[1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => [3,4,2,1,6,5]
[1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [6,3,1,5,2,4] => [3,5,2,6,4,1]
[1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [4,5,6,3,2,1]
[1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,7,5,6] => [2,1,4,3,7,8,6,5]
[1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [2,1,6,5,3,4,8,7] => [2,1,5,6,4,3,8,7]
[1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [2,1,8,5,3,7,4,6] => [2,1,5,7,4,8,6,3]
[1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [2,1,8,7,6,3,4,5] => [2,1,6,7,8,5,4,3]
[1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [4,3,1,2,6,5,8,7] => [3,4,2,1,6,5,8,7]
[1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [4,3,1,2,8,7,5,6] => [3,4,2,1,7,8,6,5]
[1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [6,3,1,5,2,4,8,7] => [3,5,2,6,4,1,8,7]
[1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [8,3,1,5,2,7,4,6] => [3,5,2,7,4,8,6,1]
[1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [8,3,1,7,6,2,4,5] => [3,6,2,7,8,5,4,1]
[1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [6,5,4,1,2,3,8,7] => [4,5,6,3,2,1,8,7]
[1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [8,5,4,1,2,7,3,6] => [4,5,7,3,2,8,6,1]
[1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [8,7,4,1,6,2,3,5] => [4,6,7,3,8,5,2,1]
[1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [5,6,7,8,4,3,2,1]
[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] => [2,1,4,3,6,5,8,7,10,9] => [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)] => [2,1,4,3,6,5,9,10,8,7] => [2,1,4,3,6,5,10,9,7,8] => [2,1,4,3,6,5,9,10,8,7]
[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] => [2,1,4,3,8,7,5,6,10,9] => [2,1,4,3,7,8,6,5,10,9]
[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] => [2,1,4,3,10,7,5,9,6,8] => [2,1,4,3,7,9,6,10,8,5]
[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] => [2,1,4,3,10,9,8,5,6,7] => [2,1,4,3,8,9,10,7,6,5]
[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] => [2,1,6,5,3,4,8,7,10,9] => [2,1,5,6,4,3,8,7,10,9]
[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] => [2,1,6,5,3,4,10,9,7,8] => [2,1,5,6,4,3,9,10,8,7]
[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] => [2,1,8,5,3,7,4,6,10,9] => [2,1,5,7,4,8,6,3,10,9]
[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] => [2,1,10,5,3,7,4,9,6,8] => [2,1,5,7,4,9,6,10,8,3]
[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] => [2,1,10,5,3,9,8,4,6,7] => [2,1,5,8,4,9,10,7,6,3]
[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] => [2,1,8,7,6,3,4,5,10,9] => [2,1,6,7,8,5,4,3,10,9]
[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] => [2,1,10,7,6,3,4,9,5,8] => [2,1,6,7,9,5,4,10,8,3]
[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] => [2,1,10,9,6,3,8,4,5,7] => [2,1,6,8,9,5,10,7,4,3]
[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] => [2,1,10,9,8,7,3,4,5,6] => [2,1,7,8,9,10,6,5,4,3]
[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] => [4,3,1,2,6,5,8,7,10,9] => [3,4,2,1,6,5,8,7,10,9]
[1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [3,4,2,1,6,5,9,10,8,7] => [4,3,1,2,6,5,10,9,7,8] => [3,4,2,1,6,5,9,10,8,7]
[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] => [4,3,1,2,8,7,5,6,10,9] => [3,4,2,1,7,8,6,5,10,9]
[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] => [4,3,1,2,10,7,5,9,6,8] => [3,4,2,1,7,9,6,10,8,5]
[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] => [4,3,1,2,10,9,8,5,6,7] => [3,4,2,1,8,9,10,7,6,5]
[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] => [6,3,1,5,2,4,8,7,10,9] => [3,5,2,6,4,1,8,7,10,9]
[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] => [6,3,1,5,2,4,10,9,7,8] => [3,5,2,6,4,1,9,10,8,7]
[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] => [8,3,1,5,2,7,4,6,10,9] => [3,5,2,7,4,8,6,1,10,9]
[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] => [10,3,1,5,2,7,4,9,6,8] => [3,5,2,7,4,9,6,10,8,1]
[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] => [10,3,1,5,2,9,8,4,6,7] => [3,5,2,8,4,9,10,7,6,1]
[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] => [8,3,1,7,6,2,4,5,10,9] => [3,6,2,7,8,5,4,1,10,9]
[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] => [10,3,1,7,6,2,4,9,5,8] => [3,6,2,7,9,5,4,10,8,1]
[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] => [10,3,1,9,6,2,8,4,5,7] => [3,6,2,8,9,5,10,7,4,1]
[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] => [10,3,1,9,8,7,2,4,5,6] => [3,7,2,8,9,10,6,5,4,1]
[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] => [6,5,4,1,2,3,8,7,10,9] => [4,5,6,3,2,1,8,7,10,9]
[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] => [6,5,4,1,2,3,10,9,7,8] => [4,5,6,3,2,1,9,10,8,7]
[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] => [8,5,4,1,2,7,3,6,10,9] => [4,5,7,3,2,8,6,1,10,9]
[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] => [10,5,4,1,2,7,3,9,6,8] => [4,5,7,3,2,9,6,10,8,1]
[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] => [10,5,4,1,2,9,8,3,6,7] => [4,5,8,3,2,9,10,7,6,1]
[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] => [8,7,4,1,6,2,3,5,10,9] => [4,6,7,3,8,5,2,1,10,9]
[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] => [10,7,4,1,6,2,3,9,5,8] => [4,6,7,3,9,5,2,10,8,1]
[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] => [10,9,4,1,6,2,8,3,5,7] => [4,6,8,3,9,5,10,7,2,1]
[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] => [10,9,4,1,8,7,2,3,5,6] => [4,7,8,3,9,10,6,5,2,1]
[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] => [8,7,6,5,1,2,3,4,10,9] => [5,6,7,8,4,3,2,1,10,9]
[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] => [10,7,6,5,1,2,3,9,4,8] => [5,6,7,9,4,3,2,10,8,1]
[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] => [10,9,6,5,1,2,8,3,4,7] => [5,6,8,9,4,3,10,7,2,1]
[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] => [10,9,8,5,1,7,2,3,4,6] => [5,7,8,9,4,10,6,3,2,1]
[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] => [10,9,8,7,6,1,2,3,4,5] => [6,7,8,9,10,5,4,3,2,1]
[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] => [2,1,4,3,6,5,8,7,10,9,12,11] => [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)] => [2,1,4,3,6,5,8,7,11,12,10,9] => [2,1,4,3,6,5,8,7,12,11,9,10] => [2,1,4,3,6,5,8,7,11,12,10,9]
[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] => [2,1,4,3,6,5,10,9,7,8,12,11] => [2,1,4,3,6,5,9,10,8,7,12,11]
[1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,9,11,8,12,10,7] => [2,1,4,3,6,5,12,9,7,11,8,10] => [2,1,4,3,6,5,9,11,8,12,10,7]
[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] => [2,1,4,3,6,5,12,11,10,7,8,9] => [2,1,4,3,6,5,10,11,12,9,8,7]
[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] => [2,1,4,3,8,7,5,6,10,9,12,11] => [2,1,4,3,7,8,6,5,10,9,12,11]
[1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,7,8,6,5,11,12,10,9] => [2,1,4,3,8,7,5,6,12,11,9,10] => [2,1,4,3,7,8,6,5,11,12,10,9]
[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] => [2,1,4,3,10,7,5,9,6,8,12,11] => [2,1,4,3,7,9,6,10,8,5,12,11]
[1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,7,9,6,11,8,12,10,5] => [2,1,4,3,12,7,5,9,6,11,8,10] => [2,1,4,3,7,9,6,11,8,12,10,5]
[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] => [2,1,4,3,12,7,5,11,10,6,8,9] => [2,1,4,3,7,10,6,11,12,9,8,5]
[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] => [2,1,4,3,10,9,8,5,6,7,12,11] => [2,1,4,3,8,9,10,7,6,5,12,11]
[1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,8,9,11,7,6,12,10,5] => [2,1,4,3,12,9,8,5,6,11,7,10] => [2,1,4,3,8,9,11,7,6,12,10,5]
[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] => [2,1,4,3,12,11,8,5,10,6,7,9] => [2,1,4,3,8,10,11,7,12,9,6,5]
[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] => [2,1,4,3,12,11,10,9,5,6,7,8] => [2,1,4,3,9,10,11,12,8,7,6,5]
[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] => [2,1,6,5,3,4,8,7,10,9,12,11] => [2,1,5,6,4,3,8,7,10,9,12,11]
[1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,5,6,4,3,8,7,11,12,10,9] => [2,1,6,5,3,4,8,7,12,11,9,10] => [2,1,5,6,4,3,8,7,11,12,10,9]
[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] => [2,1,6,5,3,4,10,9,7,8,12,11] => [2,1,5,6,4,3,9,10,8,7,12,11]
[1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,5,6,4,3,9,11,8,12,10,7] => [2,1,6,5,3,4,12,9,7,11,8,10] => [2,1,5,6,4,3,9,11,8,12,10,7]
[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] => [2,1,6,5,3,4,12,11,10,7,8,9] => [2,1,5,6,4,3,10,11,12,9,8,7]
[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] => [2,1,8,5,3,7,4,6,10,9,12,11] => [2,1,5,7,4,8,6,3,10,9,12,11]
[1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,5,7,4,8,6,3,11,12,10,9] => [2,1,8,5,3,7,4,6,12,11,9,10] => [2,1,5,7,4,8,6,3,11,12,10,9]
[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] => [2,1,10,5,3,7,4,9,6,8,12,11] => [2,1,5,7,4,9,6,10,8,3,12,11]
[1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,5,7,4,9,6,11,8,12,10,3] => [2,1,12,5,3,7,4,9,6,11,8,10] => [2,1,5,7,4,9,6,11,8,12,10,3]
[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] => [2,1,12,5,3,7,4,11,10,6,8,9] => [2,1,5,7,4,10,6,11,12,9,8,3]
[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] => [2,1,10,5,3,9,8,4,6,7,12,11] => [2,1,5,8,4,9,10,7,6,3,12,11]
[1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,5,8,4,9,11,7,6,12,10,3] => [2,1,12,5,3,9,8,4,6,11,7,10] => [2,1,5,8,4,9,11,7,6,12,10,3]
[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] => [2,1,12,5,3,11,8,4,10,6,7,9] => [2,1,5,8,4,10,11,7,12,9,6,3]
[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] => [2,1,12,5,3,11,10,9,4,6,7,8] => [2,1,5,9,4,10,11,12,8,7,6,3]
[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] => [2,1,8,7,6,3,4,5,10,9,12,11] => [2,1,6,7,8,5,4,3,10,9,12,11]
[1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,6,7,8,5,4,3,11,12,10,9] => [2,1,8,7,6,3,4,5,12,11,9,10] => [2,1,6,7,8,5,4,3,11,12,10,9]
[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] => [2,1,10,7,6,3,4,9,5,8,12,11] => [2,1,6,7,9,5,4,10,8,3,12,11]
[1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,6,7,9,5,4,11,8,12,10,3] => [2,1,12,7,6,3,4,9,5,11,8,10] => [2,1,6,7,9,5,4,11,8,12,10,3]
[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] => [2,1,12,7,6,3,4,11,10,5,8,9] => [2,1,6,7,10,5,4,11,12,9,8,3]
[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] => [2,1,10,9,6,3,8,4,5,7,12,11] => [2,1,6,8,9,5,10,7,4,3,12,11]
[1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,6,8,9,5,11,7,4,12,10,3] => [2,1,12,9,6,3,8,4,5,11,7,10] => [2,1,6,8,9,5,11,7,4,12,10,3]
[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] => [2,1,12,11,6,3,8,4,10,5,7,9] => [2,1,6,8,10,5,11,7,12,9,4,3]
[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] => [2,1,12,11,6,3,10,9,4,5,7,8] => [2,1,6,9,10,5,11,12,8,7,4,3]
>>> 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
inverse
Description
Sends a permutation to its inverse.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
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Sorry, this map was not found in the database.