Dyck Paths Enumerated by the Q-bonacci Numbers
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arXiv
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| Format: | Preprint |
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2024
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| author | Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo |
| author_facet | Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dyck Paths Enumerated by the Q-bonacci Numbers Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo Discrete Mathematics Combinatorics G.2.1 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. |
| title | Dyck Paths Enumerated by the Q-bonacci Numbers |
| topic | Discrete Mathematics Combinatorics G.2.1 |
| url | https://arxiv.org/abs/2406.16394 |