{
  "abstract": "We study the problem of determining the maximum number of stable matchings. This classical counting problem was posed by Knuth and has been studied for five decades. We obtain a new $2.999^n$ upper bound on the number of stable matchings with $n$ men and $n$ women. This improves the best-known previous result by Palmer and Pálvölgyi. This result gets much closer to the well-known lower bound $\\frac{2.28^n}{\\text{poly}(n)}$. We refine their entropy-based framework by capturing broader structural relationships among stable matchings. To capture these relationships, we introduce new frameworks, including cones and supports. This establishes the $3.332^n$ bound. We also exploit relationships among local structures and use a charging argument to improve the bound to $2.999^n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06604",
  "author_total": 3,
  "authors": [
    {
      "name": "Ken-ichi Kawarabayashi"
    },
    {
      "name": "Hikaru Wada"
    },
    {
      "name": "Masataka Yoneda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tqbvj7xxpc4r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06604",
  "fulltext_url": null,
  "id": "6tqbvj7xxpc4r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06604",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tqbvj7xxpc4r.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06604"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Sub-$3^n$ Upper Bound on the Number of Stable Matchings",
  "title_text": "A Sub-3^n Upper Bound on the Number of Stable Matchings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/6tqbvj7xxpc4r",
  "venue": "arXiv",
  "versions": []
}