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.Comment: 13 pages, 8 figures, submitted to Annals of Combinatoric