{
  "abstract": "Fishburn's latent-subset conjecture, proposed in 1987 and revisited in 1988, asserts that for every dual intersecting family $\\mathcal F\\subseteq 2^{[n]}$, there exists $i\\in[n]$ such that $|\\mathcal F^L(i)|\\geq|\\mathcal F(i)|$. Here $\\mathcal F^L$ is the family of the subsets of members of $\\mathcal F$ that do not belong to $\\mathcal F$. In this paper, we prove the conjecture using the recent weighted star inequality of Chang, Liu, and Liu.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35920",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxian Dong"
    },
    {
      "name": "Jianxi Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25pzcv12tyae1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35920",
  "fulltext_url": null,
  "id": "25pzcv12tyae1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35920",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214906947",
  "pdf_url": "https://arxiv.org/pdf/2609.35920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25pzcv12tyae1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proof of Fishburn's latent-subset conjecture",
  "title_text": "Proof of Fishburn's latent-subset conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/25pzcv12tyae1",
  "venue": "arXiv",
  "versions": []
}