Ultrahomogeneous hypertournaments

Rob Sullivan

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arXiv · 2611.07292

Ultrahomogeneous hypertournaments

Rob Sullivan

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Abstract

A $k$-hypertournament is a higher-arity generalisation of a tournament, consisting of a set together with an irreflexive $k$-ary relation such that the automorphism group of each substructure of size $k$ is the alternating group $\mathrm{A}_k$. We show that, for each $k \geq 3$, there are continuum-many non-isomorphic countable ultrahomogeneous $k$-hypertournaments, answering a question of Cherlin.

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Rob Sullivan. 2026-11-05. Ultrahomogeneous hypertournaments. https://arxiv.org/abs/2611.07292

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