On the asymptotic behavior of finite hyperfields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915876151754752 |
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| author | Le, Tuong Lowen, Chayim |
| author_facet | Le, Tuong Lowen, Chayim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the asymptotic behavior of finite hyperfields Le, Tuong Lowen, Chayim Rings and Algebras Combinatorics 12K99 (Primary), 16Y20 (Secondary) 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. |
| title | On the asymptotic behavior of finite hyperfields |
| topic | Rings and Algebras Combinatorics 12K99 (Primary), 16Y20 (Secondary) |
| url | https://arxiv.org/abs/2603.19205 |