{
  "id": "1309.6686",
  "version": "v1",
  "published": "2013-09-25T22:36:09.000Z",
  "updated": "2013-09-25T22:36:09.000Z",
  "title": "Packing Posets in the Boolean Lattice",
  "authors": [
    "Andrew P. Dove",
    "Jerrold R. Griggs"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We are interested in maximizing the number of pairwise unrelated copies of a poset $P$ in the family of all subsets of $[n]$. We prove that for any $P$ the maximum number of unrelated copies of $P$ is asymptotic to a constant times the largest binomial coefficient. Moreover, the constant has the form $\\frac{1}{c(P)}$, where $c(P)$ is the size of the smallest convex closure over all embeddings of $P$ into the Boolean lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-25T22:36:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boolean lattice",
      "packing posets",
      "unrelated copies",
      "smallest convex closure",
      "largest binomial coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6686D"
    }
  }
}