{
  "id": "1309.7379",
  "version": "v1",
  "published": "2013-09-27T22:03:08.000Z",
  "updated": "2013-09-27T22:03:08.000Z",
  "title": "Incomparable copies of a poset in the Boolean lattice",
  "authors": [
    "Gyula O. H. Katona",
    "Dániel T. Nagy"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $B_n$ be the poset generated by the subsets of $[n]$ with the inclusion as relation and let $P$ be a finite poset. We want to embed $P$ into $B_n$ as many times as possible such that the subsets in different copies are incomparable. The maximum number of such embeddings is asymptotically determined for all finite posets $P$ as $\\frac{{n \\choose \\lfloor n/2\\rfloor}}{M(P)}$, where $M(P)$ denotes the minimal size of the convex hull of a copy of $P$. We discuss both weak and strong (induced) embeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-27T22:03:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "boolean lattice",
      "incomparable copies",
      "finite poset",
      "maximum number",
      "embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7379K"
    }
  }
}