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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2510.14956 |
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| _version_ | 1866912652932939776 |
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| author | Inagaki, Ryota Pramatarova, Dimana |
| author_facet | Inagaki, Ryota Pramatarova, Dimana |
| contents | We define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic. Building on this framework, we introduce two new sequences of triangular arrays: the first one enumerates the $k$-dimensional Balanced ballot paths of exact height $s$; the second one is a new multidimensional generalization of the Narayana numbers, which count the number of Balanced ballot paths with exactly $p$ peaks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Weighted and Bounded Multidimensional Catalan Numbers Inagaki, Ryota Pramatarova, Dimana Combinatorics 05A15, 05A19, 11B50 We define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic. Building on this framework, we introduce two new sequences of triangular arrays: the first one enumerates the $k$-dimensional Balanced ballot paths of exact height $s$; the second one is a new multidimensional generalization of the Narayana numbers, which count the number of Balanced ballot paths with exactly $p$ peaks. |
| title | On Weighted and Bounded Multidimensional Catalan Numbers |
| topic | Combinatorics 05A15, 05A19, 11B50 |
| url | https://arxiv.org/abs/2510.14956 |