Elizalde, Sergi; Deutsch, Emeric A simple and unusual bijection for Dyck paths and its consequences. (English) Zbl 1047.05001 Ann. Comb. 7, No. 3, 281-297 (2003). 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. Cited in 2 ReviewsCited in 17 Documents MSC: 05A15 Exact enumeration problems, generating functions 05A05 Permutations, words, matrices Keywords:restricted permutation; Dyck paths; bijection; enumeration; statistics Software:AARON PDFBibTeX XMLCite \textit{S. Elizalde} and \textit{E. Deutsch}, Ann. Comb. 7, No. 3, 281--297 (2003; Zbl 1047.05001) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: Signature-permutation of Elizalde’s and Deutsch’s 2003 bijection for Dyck paths. Signature-permutation of the inverse of Elizalde’s and Deutsch’s 2003 bijection for Dyck paths. Signature-permutation of A057164-conjugate of Elizalde’s and Deutsch’s 2003 bijection for Dyck paths. Signature-permutation of A057164-conjugate of the inverse of Elizalde’s and Deutsch’s 2003 bijection for Dyck paths.