{
  "abstract": "We study the maximum number ${\\rm SM}(n)$ of stable matchings in an instance with $n$ men and $n$ women. Karlin, Oveis Gharan, and Weber (STOC 2018) proved the first single-exponential upper bound; their argument gives ${\\rm SM}(n)\\le 2^{17n}$ for sufficiently large $n$. Palmer and Pálvölgyi (FOCS 2021) improved this bound to $3.55^n+O(1)$. We prove that ${\\rm SM}(n)<2.81^n$. This brings the exponential base closer to $2.28$, the base of the best known lower bound. More precisely, we bound the number of stable matchings in each instance in terms of each person's number of stable partners, where a stable partner is someone matched to that person in at least one stable matching. Our proof assigns each person a weight determined by this number and uses these weights to bound the number of stable matchings by induction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06494",
  "author_total": 2,
  "authors": [
    {
      "name": "Ebrahim Ghorbani"
    },
    {
      "name": "Matthias Mnich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8v2cg0kb7jk5m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06494",
  "fulltext_url": null,
  "id": "8v2cg0kb7jk5m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06494",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/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/2611.06494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8v2cg0kb7jk5m.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A $2.81^n$ upper bound on the number of stable matchings",
  "title_text": "A 2.81^n upper bound on the number of stable matchings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/8v2cg0kb7jk5m",
  "venue": "arXiv",
  "versions": []
}