A simple and unusual bijection for Dyck paths and its consequences
arXiv:math/0306125
Abstract
In this paper we introduce a new bijection from the set of Dyck paths to itself. This bijection has the property that it maps statistics that appeared recently in the study of pattern-avoiding permutations into classical statistics on Dyck paths, whose distribution is easy to obtain. We also present a generalization of the bijection, as well as several applications of it to enumeration problems of statistics in restricted permutations.
13 pages, 8 figures, submitted to Annals of Combinatorics