{
  "abstract": "Let $k>\\ell\\ge 1$ be integers. For a family $\\mathcal{F}$ of $k$-uniform hypergraphs ($k$-graphs), its $\\ell$-degree Turán density $γ^{(k)}_\\ell(\\mathcal{F})$ is the asymptotic maximum of the normalized minimum $\\ell$-degree over all $\\mathcal{F}$-free $k$-graphs. In this paper, we prove that for all integers $k>\\ell>2$ and every $α\\in[0,1)$, there exists an infinite family $\\mathcal{F}$ of $k$-graphs such that $γ^{(k)}_\\ell(\\mathcal{F})=α$, while every finite subfamily $\\mathcal{F}'\\subset \\mathcal{F}$ satisfies $γ^{(k)}_\\ell(\\mathcal{F}')>α$. This confirms the conjecture of Mubayi and Zhao on codegree Turán densities for every $k > 3$. As an immediate consequence, the set $Γ^{k,\\ell}_{\\infty}$ of $\\ell$-degree Turán densities of nonempty $k$-graph families is $[0,1)$ whenever $k>\\ell>2$, which answers a question of Lo and Markström from 2014.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17558",
  "author_total": 2,
  "authors": [
    {
      "name": "Hao Lin"
    },
    {
      "name": "Wenling Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqdatwrhxvec0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17558",
  "fulltext_url": null,
  "id": "dqdatwrhxvec0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17558",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221821971",
  "pdf_url": "https://arxiv.org/pdf/2610.17558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqdatwrhxvec0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The $\\ell$-degree Turán densities of hypergraphs: infinite families and their finite subfamilies",
  "title_text": "The ℓ-degree Turán densities of hypergraphs: infinite families and their finite subfamilies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/dqdatwrhxvec0",
  "venue": "arXiv",
  "versions": []
}