{
  "id": "1508.05718",
  "version": "v1",
  "published": "2015-08-24T08:26:38.000Z",
  "updated": "2015-08-24T08:26:38.000Z",
  "title": "The Union-Closed Sets Conjecture for Small Families",
  "authors": [
    "Jens Maßberg"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the union-closed sets conjecture is true for separating union-closed families $\\mathcal{A}$ with $|\\mathcal{A}| \\leq 2\\left(m+\\frac{m}{\\log_2(m)-\\log_2\\log_2(m)}\\right)$ where $m$ denotes the number of elements in $\\mathcal{A}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-24T08:26:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "union-closed sets conjecture",
      "small families",
      "separating union-closed families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805718M"
    }
  }
}