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A Simple and Unusual Bijection for Dyck Paths and its Consequences
Sergi Elizalde1 and Emeric Deutsch2
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
sergi@math.mit.edu
2Polytechnic University, Brooklyn, NY 11201, USA
deutsch@duke.poly.edu
Annals of Combinatorics 7 (3) p.281-297 September, 2003
AMS Subject Classification: 05A15, 05A05
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.
Keywords: Dyck paths, bijections, restricted permutations

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