{
  "abstract": "In this paper, we study the maximal length of a minimal zero-sum sequence over $\\left[\\!\\left[ -m,m \\right]\\!\\right]^d$ having a support of size $d+1$. When $d=2$, we find the exact value of this maximal length for all $m \\ge 2$, as well as the exact structure of all extremal sequences for this problem. When $d=3$, we obtain lower and upper bounds that asymptotically match each other as $m$ tends to infinity. This allows us to improve on the best known lower bounds for the Davenport constant of low-dimensional boxes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16562",
  "author_total": 2,
  "authors": [
    {
      "name": "Benjamin Girard"
    },
    {
      "name": "Alain Plagne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mghj20vt4e64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16562",
  "fulltext_url": null,
  "id": "1mghj20vt4e64",
  "issns": [],
  "landing_url": "https://hal.science/hal-05794482v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05794482/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mghj20vt4e64.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "hal-05794482",
      "source": "hal",
      "url": "https://hal.science/hal-05794482v1"
    },
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Davenport constant of low-dimensional boxes",
  "title_text": "The Davenport constant of low-dimensional boxes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1mghj20vt4e64",
  "venue": "HAL",
  "versions": []
}