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arXiv · 2603.19205

On the asymptotic behavior of finite hyperfields

Tuong Le·Chayim Lowen
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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.

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Tuong Le, Chayim Lowen. 2026-03-19. On the asymptotic behavior of finite hyperfields. https://arxiv.org/abs/2603.19205

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