{
  "id": "1801.10431",
  "version": "v1",
  "published": "2018-01-31T13:00:32.000Z",
  "updated": "2018-01-31T13:00:32.000Z",
  "title": "On the size of the set $AA+A$",
  "authors": [
    "Oliver Roche-Newton",
    "Imre Z. Ruzsa",
    "Chun-Yen Shen",
    "Ilya D. Shkredov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "It is established that there exists an absolute constant $c>0$ such that for any finite set $A$ of positive real numbers $$|AA+A| \\gg |A|^{\\frac{3}{2}+c}.$$ On the other hand, we give an explicit construction of a finite set $A \\subset \\mathbb R$ such that $|AA+A|=o(|A|^2)$, disproving a conjecture of Balog.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-31T13:00:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite set",
      "absolute constant",
      "positive real numbers",
      "explicit construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}