{
  "id": "2310.16701",
  "version": "v1",
  "published": "2023-10-25T15:18:36.000Z",
  "updated": "2023-10-25T15:18:36.000Z",
  "title": "Odd-Sunflowers",
  "authors": [
    "Peter Frankl",
    "János Pach",
    "Dömötör Pálvölgyi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erd\\H os--Szemer\\'edi conjecture, recently proved by Naslund and Sawin, that there is a constant $\\mu<2$ such that every family of subsets of an $n$-element set that contains no odd-sunflower consists of at most $\\mu^n$ sets. We construct such families of size at least $1.5021^n$. We also characterize minimal odd-sunflowers of triples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-25T15:18:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "odd number",
      "os-szemeredi conjecture",
      "element set",
      "odd-sunflower consists",
      "characterize minimal odd-sunflowers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}