{
  "id": "2011.00915",
  "version": "v1",
  "published": "2020-11-02T11:51:40.000Z",
  "updated": "2020-11-02T11:51:40.000Z",
  "title": "At most $4.47^n$ stable matchings",
  "authors": [
    "Cory Palmer",
    "Dömötör Pálvölgyi"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We improve the upper bound for the maximum possible number of stable matchings among $n$ men and $n$ women from $O(131072^n)$ to $O(4.47^n)$. To establish this bound, we develop a novel formulation of a probabilistic technique that is easy to apply and may be of independent interest in counting other combinatorial objects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-02T11:51:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable matchings",
      "combinatorial objects",
      "upper bound",
      "independent interest",
      "probabilistic technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}