{
  "id": "1010.5042",
  "version": "v2",
  "published": "2010-10-25T06:30:41.000Z",
  "updated": "2012-08-12T19:27:46.000Z",
  "title": "On a combinatorial problem of Erdos, Kleitman and Lemke",
  "authors": [
    "Benjamin Girard"
  ],
  "comment": "15 pages",
  "journal": "Advances in Mathematics 231, 3-4 (2012) 1843-1857",
  "doi": "10.1016/j.aim.2012.06.025",
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT"
  ],
  "abstract": "In this paper, we study a combinatorial problem originating in the following conjecture of Erdos and Lemke: given any sequence of n divisors of n, repetitions being allowed, there exists a subsequence the elements of which are summing to n. This conjecture was proved by Kleitman and Lemke, who then extended the original question to a problem on a zero-sum invariant in the framework of finite Abelian groups. Building among others on earlier works by Alon and Dubiner and by the author, our main theorem gives a new upper bound for this invariant in the general case, and provides its right order of magnitude.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-12T19:27:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial problem",
      "finite abelian groups",
      "general case",
      "upper bound",
      "conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5042G"
    }
  }
}