{
  "abstract": "Let $G$ be a finite abelian group. The Erdős-Ginzburg-Ziv constant $\\mathsf{s}(G)$ is the smallest positive integer $\\ell$ such that every sequence over $G$ of length at least $\\ell$ contains a zero-sum subsequence of length $\\exp(G)$. The short zero-sum constant $η(G)$ is defined similarly, with the requirement that the zero-sum subsequence is nonempty and has length at most $\\exp(G)$. It is known that $\\mathsf{s}(G)\\ge η(G)+\\exp(G)-1.$ A conjecture proposed by W. Gao in 2003, which has been widely studied in zero-sum theory, predicts that $$ \\mathsf{s}(G)=η(G)+\\exp(G)-1 $$ for every nontrivial finite abelian group $G$. In this paper, we prove that this conjecture fails for the group $C_2^7\\oplus C_6$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01972",
  "author_total": 2,
  "authors": [
    {
      "name": "Guoqing Wang"
    },
    {
      "name": "Xiangneng Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jrsvnkvevbmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01972",
  "fulltext_url": null,
  "id": "8jrsvnkvevbmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01972",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jrsvnkvevbmj.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01972"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The equality $s(G)=η(G)+\\exp(G)-1$ fails for $G=C_2^7\\oplus C_6$",
  "title_text": "The equality s(G)=η(G)+exp(G)−1 fails for G=C_2^7⊕ C_6",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8jrsvnkvevbmj",
  "venue": "arXiv",
  "versions": []
}