{
  "id": "1606.03468",
  "version": "v1",
  "published": "2016-06-10T20:28:21.000Z",
  "updated": "2016-06-10T20:28:21.000Z",
  "title": "An improved bound on $(A+A)/(A+A)$",
  "authors": [
    "Ben Lund"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that, for a finite set $A$ of real numbers, the size of the set $$\\frac{A+A}{A+A} = \\left\\{ \\frac{a+b}{c+d} : a,b,c,d \\in A, c+d \\neq 0 \\right \\}$$ is bounded from below by $$\\left|\\frac{A+A}{A+A} \\right| \\gg \\frac{|A|^{2+1/4}}{|A / A|^{1/8} \\log |A|}.$$ This improves a result of Roche-Newton.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-10T20:28:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite set",
      "real numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}