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Ultrahomogeneous hypertournaments
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 Ak. We show that, for each k ≥ 3, there are continuum-many non-isomorphic countable ultrahomogeneous k-hypertournaments, answering a question of Cherlin.
Related
BibTeX
@misc{sullivan2026ultrahomogeneous,
title = {{Ultrahomogeneous hypertournaments}},
author = {Rob Sullivan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07292},
eprint = {2611.07292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07292},
}
RIS
TY - UNPB
TI - Ultrahomogeneous hypertournaments
AU - Rob Sullivan
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07292
UR - https://arxiv.org/abs/2611.07292
AB - 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 A_k. We show that, for each k ≥ 3, there are continuum-many non-isomorphic countable ultrahomogeneous k-hypertournaments, answering a question of Cherlin.
ER -