{
  "abstract": "Let $k>\\ell\\ge 1$ be integers. For a family $\\mathcal{F}$ of $k$-uniform hypergraphs ($k$-graphs), the $\\ell$-degree Turán density $γ^{(k)}_\\ell(\\mathcal{F})$ of $\\mathcal{F}$ is defined as the asymptotic maximum of the normalized minimum $\\ell$-degree over all $\\mathcal{F}$-free $k$-graphs. In this paper, we prove that for all $k>\\ell>k/2$, every rational number $α\\in[0,1)$ can be realized as the $\\ell$-degree Turán density $γ^{(k)}_\\ell(\\mathcal{F})$ for some finite family $\\mathcal{F}$ of $k$-graphs. Furthermore, for any $k>\\ell\\ge 1$, we construct an explicit infinite sequence of values realized by single forbidden $k$-graphs: for each integer $q\\ge2$, there exists a $k$-graph $F$ such that $γ^{(k)}_\\ell(F)=1-q^{\\ell-k}$. We also establish a strengthened non-principality property for $\\ell$-degree Turán densities: for all $k>\\ell>1$, there exist two $k$-graphs $F_1$ and $F_2$ satisfying $0< γ^{(k)}_{\\ell}(\\{F_1,F_2\\})<\\min\\{ γ^{(k)}_\\ell(F_1),γ^{(k)}_\\ell(F_2)\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18927",
  "author_total": 2,
  "authors": [
    {
      "name": "Quanyu Tang"
    },
    {
      "name": "Wenling Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04bmj7hqr515f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18927",
  "fulltext_url": null,
  "id": "04bmj7hqr515f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18927",
  "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": "W7213497878",
  "pdf_url": "https://arxiv.org/pdf/2609.18927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04bmj7hqr515f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18927"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Rational values and non-principality for $\\ell$-degree Turán densities of hypergraphs",
  "title_text": "Rational values and non-principality for ℓ-degree Turán densities of hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/04bmj7hqr515f",
  "venue": "arXiv",
  "versions": []
}