{
  "abstract": "In response to a conjecture of Petr and Turek, we prove that every largest intersecting temperate collection of sets $\\mathcal{A}\\subseteq [2k]^{(k)}\\cup [2k]^{(k+1)}\\cup [2k]^{(k+2)}$ includes all $k$-sets containing some given $a\\in[2k]$, all $(k+1)$-sets, and all $(k+2)$-sets not containing $a$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24747",
  "author_total": 1,
  "authors": [
    {
      "name": "Kada Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bn3qfp36s08r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24747",
  "fulltext_url": null,
  "id": "5bn3qfp36s08r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24747",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214002263",
  "pdf_url": "https://arxiv.org/pdf/2609.24747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bn3qfp36s08r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Three-Layer Intersecting Temperate Families",
  "title_text": "Three-Layer Intersecting Temperate Families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5bn3qfp36s08r",
  "venue": "arXiv",
  "versions": []
}