{
  "abstract": "For a prime power $q\\geq2$ and an integer $m\\geq2$, let $PG(m,q)$ denote the $m-$dimensional projective hypergraph over the finite field $\\mathbb{F}_q$. Employing the $\\mathsf{L}^p-$method and using the incidence structure, we establish the Turán density of $PG(m,q)$ \\begin{equation*} π(PG(m,q))\\leq\\begin{cases} \\left(1-\\frac{1}{q+1}\\right)^{\\frac{1}{q}} & \\text{ if } m=2, \\left(1-\\frac{1}{(q+1)|E(PG(m-1,q))|}\\right)^{\\frac{1}{1+q^{m-1}}} & \\text{ if } m\\geq3. \\end{cases} \\end{equation*} The previously known upper bound on its Turán density was $1-\\binom{q^m}{q}^{-1}$. As a consequence of our estimate, this upper bound is improved for each prime power $q\\geq3$ and for each dimension index $m\\geq2$. For a positive integer $t$, let $B_{t}[PG(2,q)]$ be the $(q+1)-$graph formed by taking $t$ copies of the $PG(2,q)$ that shares a common edge. Using the $\\mathsf{L}^p-$method, we establish that the upper bound of the Turán density of $B_{t}[PG(2,q)]$ is $\\left(1-\\frac{1}{q+1}\\right)^{\\frac{1}{qt}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01084",
  "author_total": 2,
  "authors": [
    {
      "name": "Subhankar Dash"
    },
    {
      "name": "Kaushik Majumder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g04janmwm5xx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01084",
  "fulltext_url": null,
  "id": "4g04janmwm5xx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01084",
  "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": "W7215752385",
  "pdf_url": "https://arxiv.org/pdf/2610.01084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g04janmwm5xx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Upper Bounds on the Turán Density of Hypergraphs Associated with the Projective Plane over a Finite Field",
  "title_text": "Upper Bounds on the Turán Density of Hypergraphs Associated with the Projective Plane over a Finite Field",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/4g04janmwm5xx",
  "venue": "arXiv",
  "versions": []
}