English

Dyck Paths Enumerated by the Q-bonacci Numbers

Discrete Mathematics 2024-06-25 v1 Combinatorics

Abstract

We consider Dyck paths having height at most two with some constraints on the number of consecutive valleys at height one which must be followed by a suitable number of valleys at height zero. We prove that they are enumerated by so-called Q-bonacci numbers (recently introduced by Kirgizov) which generalize the classical q-bonacci numbers in the case where q is a positive rational.

Cite

@article{arxiv.2406.16394,
  title  = {Dyck Paths Enumerated by the Q-bonacci Numbers},
  author = {Elena Barcucci and Antonio Bernini and Stefano Bilotta and Renzo Pinzani},
  journal= {arXiv preprint arXiv:2406.16394},
  year   = {2024}
}

Comments

In Proceedings GASCom 2024, arXiv:2406.14588

R2 v1 2026-06-28T17:16:53.742Z