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arXiv · 2409.20210

Rational Dyck paths

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

Given a positive rational $q$, we consider Dyck paths having height at most two with some constraints on the number of consecutive peaks and consecutive valleys, depending on $q$. 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 $\mathbb Q$-bonacci numbers.

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Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani. 2024-09-30. Rational Dyck paths. https://arxiv.org/abs/2409.20210

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