Restricted Dumont permutations, Dyck paths, and noncrossing partitions

Details Restricted Dumont permutations, Dyck paths, and noncrossing partitions Restricted Dumont permutations, Dyck paths, and noncrossing partitions

2006-10-06

arxiv.org/abs/math/0610234v1

Discrete Mathematics 306 (2006), 2851 to 2869

Mathematics

Combinatorics

20 pages, 5 figures

Scientific paper

We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths. Finally, we enumerate Dumont permutations of the first kind simultaneously avoiding certain pairs of 4-letter patterns and another pattern of arbitrary length.

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