{
  "id": "2301.04219",
  "version": "v1",
  "published": "2023-01-10T21:50:50.000Z",
  "updated": "2023-01-10T21:50:50.000Z",
  "title": "Extensions of a Family for Sunflowers",
  "authors": [
    "Junichiro Fukuyama"
  ],
  "comment": "This paper shows another proof of the sunflower conjecture that is different from the one present in arXiv:2212.13609 [math.CO]. Extra information on the two papers is available at Penn State Sites: https://sites.psu.edu/sunflowerconjecture/2023/01/10/index-page/,",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper refines the original construction of the recent proof of the sunflower conjecture to prove the same general bound $[ ck \\log (k+1) ]^m$ on the cardinality of a family of $m$-cardinality sets without a sunflower of $k$ elements. Our proof uses a structural claim on an extension of a family that has been previously developed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-10T21:50:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "general bound",
      "original construction",
      "paper refines",
      "sunflower conjecture",
      "cardinality sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}