{
  "id": "0704.0541",
  "version": "v1",
  "published": "2007-04-04T10:36:01.000Z",
  "updated": "2007-04-04T10:36:01.000Z",
  "title": "On complete subsets of the cyclic group",
  "authors": [
    "Y. O. Hamidoune",
    "A. S. Lladó",
    "O. Serra"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A subset $X$ of an abelian $G$ is said to be {\\em complete} if every element of the subgroup generated by $X$ can be expressed as a nonempty sum of distinct elements from $X$. Let $A\\subset \\Z_n$ be such that all the elements of $A$ are coprime with $n$. Solving a conjecture of Erd\\H{o}s and Heilbronn, Olson proved that $A$ is complete if $n$ is a prime and if $|A|>2\\sqrt{n}.$ Recently Vu proved that there is an absolute constant $c$, such that for an arbitrary large $n$, $A$ is complete if $|A|\\ge c\\sqrt{n},$ and conjectured that 2 is essentially the right value of $c$. We show that $A$ is complete if $|A|> 1+2\\sqrt{n-4}$, thus proving the last conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-04T10:36:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75",
      "20D60"
    ],
    "keywords": [
      "cyclic group",
      "complete subsets",
      "conjecture",
      "right value",
      "distinct elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.0541H"
    }
  }
}