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On the largest sum-free subset of the lattice cube

Combinatorics 2026-05-04 v1 Number Theory

Abstract

We determine the limiting density of the largest sum-free subset of the lattice cube {1,2,,n}d\{1,2,\ldots,n\}^d for all dd, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices.

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Cite

@article{arxiv.2605.00816,
  title  = {On the largest sum-free subset of the lattice cube},
  author = {Peter Keevash and Jeck Lim},
  journal= {arXiv preprint arXiv:2605.00816},
  year   = {2026}
}

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17 pages