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arXiv · 2307.02837

Restricting Dyck Paths and 312-avoiding Permutations

Elena Barcucci·Antonio Bernini·Stefano Bilotta·Renzo Pinzani
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Abstract

Dyck paths having height at most $h$ and without valleys at height $h-1$ are combinatorially interpreted by means of 312-avoding permutations with some restrictions on their \emph{left-to-right maxima}. The results are obtained by analyzing a restriction of a well-known bijection between the sets of Dyck paths and 312-avoding permutations. We also provide a recursive formula enumerating these two structures using ECO method and the theory of production matrices. As a further result we obtain a family of combinatorial identities involving Catalan numbers.

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Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani. 2023-07-06. Restricting Dyck Paths and 312-avoiding Permutations. https://arxiv.org/abs/2307.02837

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