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arXiv · 2508.08865

Formulas and asymptotics of hypergraph Catalan numbers

Eva-Maria Hainzl
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Abstract

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.

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Eva-Maria Hainzl. 2026-03-23. Formulas and asymptotics of hypergraph Catalan numbers. https://arxiv.org/abs/2508.08865

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