{
  "id": "1108.4373",
  "version": "v1",
  "published": "2011-08-22T16:36:56.000Z",
  "updated": "2011-08-22T16:36:56.000Z",
  "title": "Three layer $Q_2$-free families in the Boolean lattice",
  "authors": [
    "Jacob Manske",
    "Jian Shen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the largest $Q_2$-free family of subsets of $[n]$ which contains sets of at most three different sizes has at most $(3 + 2\\sqrt {3})N/3 + o(N) \\approx 2.1547N + o(N)$ members, where $N = {n \\choose {\\lfloor n/2 \\rfloor}}$. This improves an earlier bound of $2.207N + o(N)$ by Axenovich, Manske, and Martin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-22T16:36:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boolean lattice",
      "free family",
      "earlier bound",
      "contains sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4373M"
    }
  }
}