Restricting Dyck Paths and 312-avoiding Permutations
Combinatorics
2023-07-07 v1
Abstract
Dyck paths having height at most and without valleys at height 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.
Cite
@article{arxiv.2307.02837,
title = {Restricting Dyck Paths and 312-avoiding Permutations},
author = {Elena Barcucci and Antonio Bernini and Stefano Bilotta and Renzo Pinzani},
journal= {arXiv preprint arXiv:2307.02837},
year = {2023}
}