{
  "id": "0911.4204",
  "version": "v2",
  "published": "2009-11-21T21:40:18.000Z",
  "updated": "2010-08-26T21:14:05.000Z",
  "title": "Maximal independent sets and separating covers",
  "authors": [
    "Vincent Vatter"
  ],
  "comment": "To appear in the Monthly",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which is the product of positive integers with sum n? We give a combinatorial explanation for this relationship, via Moon and Moser's answer to a question of Erdos: how many maximal independent sets can a graph on n vertices have? We conclude by showing how Moon and Moser's solution also sheds light on a problem of Mahler and Popken's about the complexity of integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-26T21:14:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal independent sets",
      "separating cover",
      "katonas question turns",
      "simpler question",
      "largest integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4204V"
    }
  }
}