{
  "id": "1812.00537",
  "version": "v1",
  "published": "2018-12-03T03:18:32.000Z",
  "updated": "2018-12-03T03:18:32.000Z",
  "title": "Bollobás-type inequalities on set $k$-tuples",
  "authors": [
    "Jason O'Neill",
    "Jacques Verstraete"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Bollob\\'as set pairs inequality is a fundamental result in extremal set theory. In this paper, we examine suitable conditions on $k$-wise intersections from a $k$-tuple of set families for which a Bollob\\'as-type inequality holds. We then use the standard connection between extremal set theory and covering problems to give lower and upper bounds on the biclique covering numbers of a few particular $k$-uniform hypergraphs. We also provide random and explicit constructions of these Bollob\\'as set $k$-tuples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-03T03:18:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65"
    ],
    "keywords": [
      "bollobás-type inequalities",
      "extremal set theory",
      "bollobas set pairs inequality",
      "bollobas-type inequality holds",
      "fundamental result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}