Rational Dyck paths
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912051742375936 |
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| author | Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo |
| author_facet | Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational Dyck paths Barcucci, Elena Bernini, Antonio Bilotta, Stefano Pinzani, Renzo Combinatorics 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. |
| title | Rational Dyck paths |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.20210 |