{
  "id": "1106.3421",
  "version": "v1",
  "published": "2011-06-17T09:16:15.000Z",
  "updated": "2011-06-17T09:16:15.000Z",
  "title": "Beyond sum-free sets in the natural numbers",
  "authors": [
    "Sophie Huczynska"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an interval [1,N] in the natural numbers, investigating subsets S of [1,N] such that |{(x,y) in S^2:x+y in S}|=0, known as sum-free sets, has attracted considerable attention. In this paper, we define r(S):=|{(x,y) in S^2: x+y in S}| and consider its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable r-values for the s-sets of [1,N], constructive existence results and structural characterizations for sets attaining extremal and near-extremal values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-17T09:16:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75"
    ],
    "keywords": [
      "sum-free sets",
      "natural numbers",
      "constructive existence results",
      "structural characterizations",
      "sets attaining extremal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3421H"
    }
  }
}