Large sum-free sets in finite vector spaces II
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914442788208640 |
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| author | Reiher, Christian Zotova, Sofia |
| author_facet | Reiher, Christian Zotova, Sofia |
| contents | Answering a question of Leo Versteegen, we prove that for $n\ge 3$ every sum-free set $A\subseteq\mathbb{F}_5^n$ with $|A|\ge 28\cdot 5^{n-3}$ is either contained in the union of two parallel hyperplanes, or isomorphic to $Λ\times \mathbb{F}_5^{n-3}$, where $Λ\subseteq \mathbb{F}_5^3$ denotes a certain sum-free set of size $28$ discovered by Vsevolod Lev and Leo Versteegen. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large sum-free sets in finite vector spaces II Reiher, Christian Zotova, Sofia Combinatorics Number Theory 11B13, 11B30, 11P70 Answering a question of Leo Versteegen, we prove that for $n\ge 3$ every sum-free set $A\subseteq\mathbb{F}_5^n$ with $|A|\ge 28\cdot 5^{n-3}$ is either contained in the union of two parallel hyperplanes, or isomorphic to $Λ\times \mathbb{F}_5^{n-3}$, where $Λ\subseteq \mathbb{F}_5^3$ denotes a certain sum-free set of size $28$ discovered by Vsevolod Lev and Leo Versteegen. |
| title | Large sum-free sets in finite vector spaces II |
| topic | Combinatorics Number Theory 11B13, 11B30, 11P70 |
| url | https://arxiv.org/abs/2604.02894 |