{
  "id": "1303.4065",
  "version": "v1",
  "published": "2013-03-17T14:52:41.000Z",
  "updated": "2013-03-17T14:52:41.000Z",
  "title": "A construction of almost Steiner systems",
  "authors": [
    "Asaf Ferber",
    "Rani Hod",
    "Michael Krivelevich",
    "Benny Sudakov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $n$, $k$, and $t$ be integers satisfying $n>k>t\\ge2$. A Steiner system with parameters $t$, $k$, and $n$ is a $k$-uniform hypergraph on $n$ vertices in which every set of $t$ distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for $t\\geq6$. In this note we prove that for every $k>t\\ge2$ and sufficiently large $n$, there exists an almost Steiner system with parameters $t$, $k$, and $n$; that is, there exists a $k$-uniform hypergraph on $n$ vertices such that every set of $t$ distinct vertices is covered by either one or two edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-17T14:52:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "construction",
      "uniform hypergraph",
      "distinct vertices",
      "nontrivial steiner system",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4065F"
    }
  }
}