{
  "abstract": "For a nontrivial finite abelian group $G$, let $ν(G)$ be the smallest {nonnegative} integer $\\ell$ such that every zero-sum free sequence $T$ over $G$ of length at least $\\ell$ has the following property: all nonzero elements of $G$ that do not occur as a subsequence sum of $T$ lie in a proper coset of some subgroup of $G$. It is easy to check that $\\mathsf d (G)-1 \\le ν(G) \\le \\mathsf d (G)$, where $\\mathsf d (G)$ is the small Davenport constant of $G$. A conjecture by Gao from the year 2000 stated that equality should always hold at the lower bound. This conjecture has since been confirmed for many families of groups (including all p-groups and groups of rank at most two). In this paper, we disprove the conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17127",
  "author_total": 3,
  "authors": [
    {
      "name": "Alfred Geroldinger"
    },
    {
      "name": "Guoqing Wang"
    },
    {
      "name": "Wenkai Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fg7cpwgfyf00k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17127",
  "fulltext_url": null,
  "id": "fg7cpwgfyf00k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17127",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213428853",
  "pdf_url": "https://arxiv.org/pdf/2609.17127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fg7cpwgfyf00k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2609.17127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17127"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On a classical zero-sum invariant II: Disproof of a long-standing conjecture",
  "title_text": "On a classical zero-sum invariant II: Disproof of a long-standing conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fg7cpwgfyf00k",
  "venue": "arXiv",
  "versions": []
}