{
  "id": "1211.3341",
  "version": "v2",
  "published": "2012-11-14T15:57:41.000Z",
  "updated": "2013-02-18T08:53:25.000Z",
  "title": "Maximal sets with no solution to x+y=3z",
  "authors": [
    "Alain Plagne",
    "Anne de Roton"
  ],
  "comment": "Lemma 4 has been corrected. More information is given on the reference [2] in the introduction",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper, we are interested in a generalization of the notion of sum-free sets. We address a conjecture first made in the 90s by Chung and Goldwasser. Recently, after some computer checks, this conjecture was formulated again by Matolcsi and Ruzsa, who made a first significant step towards it. Here, we prove the full conjecture by giving an optimal upper bound for the Lebesgue measure of a 3-sum-free subset A of [0,1], that is, a set containing no solution to the equation x+y=3z where x,y and z are restricted to belong to A. We then address the inverse problem and characterize precisely, among all sets with that property, those attaining the maximal possible measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-18T08:53:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal sets",
      "first significant step",
      "optimal upper bound",
      "computer checks",
      "inverse problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3341P"
    }
  }
}