{
  "abstract": "Let $\\mathsf D(G)$ denote the Davenport constant of a finite abelian group $G$, the maximal length of a minimal zero-sum sequence over $G$. Gao and Geroldinger conjectured that every minimal zero-sum sequence of length $\\mathsf D(G)$~\\cite[Conjecture~6.1]{GG99} and every zero-sumfree sequence of length $\\mathsf D(G)-1$~\\cite[Conjecture~4.1]{GG06} contains an element of order $\\exp(G)$. We disprove both conjectures by proving a density-one theorem: for every fixed finite abelian group $H$ of exponent $M=2^ap^b$, where $a\\ge2$, $b\\ge1$, and $p$ is an odd prime, the set of integers $r\\ge0$ for which $G_r=C_2^r\\oplus H$ admits a minimal zero-sum sequence of length $\\mathsf D(G_r)$ with no term of order $M$ has natural density one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02063",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongke Qu"
    },
    {
      "name": "Guoqing Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hqvfj0epwz7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02063",
  "fulltext_url": null,
  "id": "0hqvfj0epwz7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02063",
  "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/2611.02063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hqvfj0epwz7z.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal zero-sum sequences without elements of maximal order",
  "title_text": "Extremal zero-sum sequences without elements of maximal order",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0hqvfj0epwz7z",
  "venue": "arXiv",
  "versions": []
}