On the largest sum-free subset of the lattice cube
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866918477541933056 |
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| author | Keevash, Peter Lim, Jeck |
| author_facet | Keevash, Peter Lim, Jeck |
| contents | We determine the limiting density of the largest sum-free subset of the lattice cube $\{1,2,\ldots,n\}^d$ for all $d$, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the largest sum-free subset of the lattice cube Keevash, Peter Lim, Jeck Combinatorics Number Theory 05D05 We determine the limiting density of the largest sum-free subset of the lattice cube $\{1,2,\ldots,n\}^d$ for all $d$, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices. |
| title | On the largest sum-free subset of the lattice cube |
| topic | Combinatorics Number Theory 05D05 |
| url | https://arxiv.org/abs/2605.00816 |