Formulas and asymptotics of hypergraph Catalan numbers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912978102648832 |
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| author | Hainzl, Eva-Maria |
| author_facet | Hainzl, Eva-Maria |
| contents | Tree walks are a class of closed walks on a complete graph constrained to span trees. In this work, we focus on a special subclass called $k$-tours, which were recently introduced by Gunnells and are enumerated by the hypergraph Catalan numbers $ c_n^{(k)}$. Gunnells conjectured an asymptotic formula for $c_n^{(k)}$ which we confirm through an alternative approach to their enumeration. As it turns out, the asymptotic growth is governed by the number of $k$-tours on star-like trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formulas and asymptotics of hypergraph Catalan numbers Hainzl, Eva-Maria Combinatorics Tree walks are a class of closed walks on a complete graph constrained to span trees. In this work, we focus on a special subclass called $k$-tours, which were recently introduced by Gunnells and are enumerated by the hypergraph Catalan numbers $ c_n^{(k)}$. Gunnells conjectured an asymptotic formula for $c_n^{(k)}$ which we confirm through an alternative approach to their enumeration. As it turns out, the asymptotic growth is governed by the number of $k$-tours on star-like trees. |
| title | Formulas and asymptotics of hypergraph Catalan numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.08865 |