{
  "annotation_id": "65cdc248-9f94-40d6-9e64-34975f12218d",
  "date_created": "2026-02-17T05:53:12.322000Z",
  "date_modified": "2026-02-17T05:53:12.322000Z",
  "file_hash": "50250431b3fccf1b9cd3d8ddc544c1fbe1a49899724e8a8442a3105ea5af3252",
  "private": false,
  "record": {
    "abstract": "For two positive integers $m$ and $M$, we study the Davenport constant of the interval of integers $[\\![ -m,M ]\\!]$, that is the maximal length of a minimal zero-sum sequence composed of elements from $[\\![ -m,M ]\\!]$. We prove the conjecture that it is equal to $m+M- r$ where $r$ is the smallest integer which can be decomposed as a sum of two non-negative integers $t_1$ and $t_2$ ($r=t_1+t_2$) having the property that $\\gcd (M-t_1, m-t_2)=1$.",
    "arxiv_id": "2601.07950",
    "authors": [
      "Benjamin Girard",
      "Alain Plagne"
    ],
    "categories": [
      "math.NT",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "The Davenport constant of an interval: a proof that $\\mathsf{D}=\\chi$",
    "url": "https://arxiv.org/abs/2601.07950",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bd38cf52-db82-4955-9b18-c34f53fd066c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}