Rational Dyck paths
Combinatorics
2024-10-01 v1
Abstract
Given a positive rational , we consider Dyck paths having height at most two with some constraints on the number of consecutive peaks and consecutive valleys, depending on . We introduce a general class of Dyck paths, called rational Dyck paths, and provide the associated generating function, according to their semilength, as well as the construction of such a class. Moreover, we characterize some subsets of the rational Dyck paths that are enumerated by the -bonacci numbers.
Cite
@article{arxiv.2409.20210,
title = {Rational Dyck paths},
author = {Elena Barcucci and Antonio Bernini and Stefano Bilotta and Renzo Pinzani},
journal= {arXiv preprint arXiv:2409.20210},
year = {2024}
}