On the asymptotic behavior of finite hyperfields
Rings and Algebras
2026-03-23 v1 Combinatorics
Abstract
Hobby has recently shown that almost all finite hyperfields of even order fail to be the quotient of a field. Using a probabilistic argument, we extend this result to all orders: a finite hyperfield is almost always non-quotient. This confirms a conjecture of Baker--Jin. We show that in almost every finite hyperfield the sum of any four or more nonzero elements contains 0. We also give a precise asymptotic for the number of finite hyperfields on a given finite abelian group.
Keywords
Cite
@article{arxiv.2603.19205,
title = {On the asymptotic behavior of finite hyperfields},
author = {Tuong Le and Chayim Lowen},
journal= {arXiv preprint arXiv:2603.19205},
year = {2026}
}
Comments
21 pages, 1 figure