{
  "abstract": "Let $V$ be an $n$-dimensional vector space over a finite field of order $q$. Let $r\\geq 3$, $(r-1)n\\geq rk$ and let $\\mathcal F_1,\\ldots,\\mathcal F_r\\subset \\genfrac{[}{]}{0pt}{}{V}{k}$, where $\\genfrac{[}{]}{0pt}{}{V}{k}$ denotes the set of $k$-dimensional subspaces of $V$. Suppose that $F_1\\cap\\cdots\\cap F_r\\neq\\{0\\}$ holds for all $F_i\\in\\mathcal F_i$, $1\\leq i\\leq r$. Then we show that $\\prod_{i=1}^r|\\mathcal F_i|\\leq\\genfrac{[}{]}{0pt}{}{n-1}{k-1}$, provided $n-k$ is sufficiently large for fixed $q$ and $r$. Moreover, equality holds if and only if there is a common line $L$ such that every family $\\mathcal F_i$ consists of all $k$-dimensional subspaces containing the line $L$. One of the main tools of the proof is a junta theorem concerning intersecting linear maps obtained by Ellis, Kindler, and Lifshitz.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28013",
  "author_total": 2,
  "authors": [
    {
      "name": "Toshihiro Shimizu"
    },
    {
      "name": "Norihide Tokushige"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6705den7hkar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28013",
  "fulltext_url": null,
  "id": "a6705den7hkar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28013",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7204806577",
  "pdf_url": "https://arxiv.org/pdf/2608.28013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6705den7hkar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A product theorem for $r$-cross intersecting families of subspaces",
  "title_text": "A product theorem for r-cross intersecting families of subspaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/a6705den7hkar",
  "venue": "arXiv",
  "versions": []
}