{
  "abstract": "For a positive integer $k$, let $f(k)$ be the minimum number of distinct nonempty subset sums of a zero-sum-free $k$-element set, where the minimum is taken over all finite abelian groups. We prove $f(k)\\ge \\frac{k^2}{2}-13k\\log(k+1)-116k$. Together with the classical upper bound, this gives $f(k)=k^2/2+O(k\\log k)$, with the optimal leading coefficient. As a consequence, the Olson constant of every finite abelian group $G$ satisfies $\\mathrm{Ol}(G)\\le\\sqrt{2|G|}+O(\\log|G|)$. The argument combines a triangular lower bound for repeated supports, a count using blocks of two and three copies, and a greedy expansion argument. No restriction is imposed on the order of the group or on the stabilizer of the set of subset sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38373",
  "author_total": 1,
  "authors": [
    {
      "name": "Chao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7arbe2e5f13vj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38373",
  "fulltext_url": null,
  "id": "7arbe2e5f13vj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38373",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38373",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7arbe2e5f13vj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38373",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38373"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A logarithmic error term for subset sums of zero-sum-free sets",
  "title_text": "A logarithmic error term for subset sums of zero-sum-free sets",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7arbe2e5f13vj",
  "venue": "arXiv",
  "versions": []
}