{
  "abstract": "Given an additively written abelian group $G$ and a set $X\\subseteq G$, we let $\\mathsf{D}(X)$ denote the Davenport constant of $X$, namely the largest non-negative integer $n$ for which there exists a sequence $x_1, \\dots, x_n$ of elements of $X$ such that $\\sum_{i=1}^n x_i =0$ and $\\sum_{i \\in I} x_i \\ne 0$ for each non-empty proper subset $I$ of $\\{1, \\ldots, n\\}$. In this paper, we mainly investigate the case when $G$ is $\\mathbb{Z}^2$ and $\\mathbb{Z}^3$, and $X$ is a discrete Euclidean ball. An application to the classical problem of estimating the Davenport constant of a box - a product of intervals of integers - is then obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Benjamin Girard"
    },
    {
      "name": "Alain Plagne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19s0wsjpg57ky.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "19s0wsjpg57ky",
  "issns": [],
  "landing_url": "https://hal.science/hal-05328809v2",
  "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": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
    ],
    [
      "hal",
      "1.math.math-nt"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05328809/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19s0wsjpg57ky.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:51Z",
      "native_id": "hal-05328809",
      "source": "hal",
      "url": "https://hal.science/hal-05328809v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Davenport constant of balls and boxes",
  "title_text": "The Davenport constant of balls and boxes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:51Z",
  "url": "https://research.draconitic.com/paper/19s0wsjpg57ky",
  "venue": "HAL",
  "versions": []
}