{
  "annotation_id": "e5fc83c2-3602-42fd-864a-885771bd7002",
  "date_created": "2026-02-17T05:53:07.571000Z",
  "date_modified": "2026-02-17T05:53:07.571000Z",
  "file_hash": "8a5d5f4339f04b6f61f35d3dde68f85c6078548d8235ae0a913b68f354d58f8f",
  "private": false,
  "record": {
    "abstract": "Let $ex_r(N,g)$ be the maximum number of edges in an $r$-uni\\-form hypergraph on $N$ vertices with girth at least $g$. We are interested in the asymptotic behavior of this value when $N$ is increasing but parameters $g\\in\\{6,8\\}$ and $r\\geq3$ are fixed. It is shown that for some positive constants $c$ and $d$, any integer $r\\geq3$ and all sufficiently large integers $N$ the inequalities $ex_r(N,6)\\geq N^{\\frac{11}{8}-\\frac{c}{\\sqrt{\\log N}}}$ and $ex_r(N,8)\\geq N^{\\frac{11}{9}-\\frac{d}{\\sqrt{\\log N}}}$ hold.",
    "arxiv_id": "2601.06374",
    "authors": [
      "Nikolai Parvatov"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Uniform hypergraphs of girth $6$ and $8$ from generalized polygons",
    "url": "https://arxiv.org/abs/2601.06374",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0b08782b-7509-488b-9282-f7ac678b4dd9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}