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A simple and unusual bijection for Dyck paths and its consequences. (English) Zbl 1047.05001

Summary: 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.

MSC:

05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices

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