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A simple and unusual bijection for Dyck paths and its consequences

Sergi Elizalde·Emeric Deutsch
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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.

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Sergi Elizalde, Emeric Deutsch. 2003-06-09. A simple and unusual bijection for Dyck paths and its consequences. https://arxiv.org/abs/math/0306125

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