{
  "annotation_id": "06383421-0e6e-4d0a-95cd-a6f4757a8043",
  "date_created": "2026-02-17T05:53:24.383000Z",
  "date_modified": "2026-02-17T05:53:24.383000Z",
  "file_hash": "408ee1574a48b7179211125d20c3268104f3466c93a2fac004ac88ca27eb4065",
  "private": false,
  "record": {
    "abstract": "A set of points $S \\subseteq \\mathbb{F}_p^n$ is called \\emph{$p$-divisible} if every affine hyperplane in $\\mathbb{F}_p^n$ intersects $S$ in $0 \\pmod p$ points. The Strong Cylinder Conjecture of Ball asserts that if\n  $S$ is a $p$-divisible set of $p^2$ points in $\\mathbb{F}_p^3$, then $S$ is a cylinder. In this paper, we show that every $p$-divisible multiset $S$ is both a $\\mathbb{F}_p$-linear and $\\mathbb{Z}$-linear combination of characteristic functions of cylinders. In addition, the multisets of size $p^2$ are $\\Z$-linear combinations of a plane and weighted differences of parallel lines.",
    "arxiv_id": "2601.09910",
    "authors": [
      "Gergely Kiss",
      "\u00c1d\u00e1m Mark\u00f3",
      "Zolt\u00e1n L\u00f3r\u00e1nt Nagy",
      "G\u00e1bor Somlai"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Cylinder type and $p$-divisible sets in $\\mathbb{F}_p^3$",
    "url": "https://arxiv.org/abs/2601.09910",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "503e1b7a-8af3-4848-bce2-20097253b696",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}