{
  "id": "1401.6390",
  "version": "v1",
  "published": "2014-01-24T16:18:44.000Z",
  "updated": "2014-01-24T16:18:44.000Z",
  "title": "Følner sequences and sum-free sets",
  "authors": [
    "Sean Eberhard"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Erd\\H{o}s showed that every set of $n$ positive integers contains a subset of size at least $n/(k+1)$ containing no solutions to $x_1 + \\cdots + x_k = y$. We prove that the constant $1/(k+1)$ here is best possible by showing that if $(F_m)$ is a multiplicative F{\\o}lner sequence in $\\mathbf{N}$ then $F_m$ has no $k$-sum-free subset of size greater than $(1/(k+1)+o(1))|F_m|$. This provides a new proof and a generalisation of a recent theorem of Eberhard, Green, and Manners.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-24T16:18:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sum-free sets",
      "følner sequences",
      "positive integers contains",
      "sum-free subset",
      "size greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6390E"
    }
  }
}