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2006

Restricted Dumont permutations, Dyck paths, and noncrossing partitions

9 years 11 months ago
Restricted Dumont permutations, Dyck paths, and noncrossing partitions
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.
Alexander Burstein, Sergi Elizalde, Toufik Mansour
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DM
Authors Alexander Burstein, Sergi Elizalde, Toufik Mansour
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