{
  "id": "1110.1961",
  "version": "v2",
  "published": "2011-10-10T08:48:37.000Z",
  "updated": "2012-06-26T18:50:05.000Z",
  "title": "k-Sums in abelian groups",
  "authors": [
    "Benjamin Girard",
    "Simon Griffiths",
    "Yahya Ould Hamidoune"
  ],
  "comment": "15 pages",
  "journal": "Combinatorics, Probability and Computing 21, 4 (2012) 582-596",
  "doi": "10.1017/S0963548312000168",
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT"
  ],
  "abstract": "Given a finite subset A of an abelian group G, we study the set k \\wedge A of all sums of k distinct elements of A. In this paper, we prove that |k \\wedge A| >= |A| for all k in {2,...,|A|-2}, unless k is in {2,|A|-2} and A is a coset of an elementary 2-subgroup of G. Furthermore, we characterize those finite subsets A of G for which |k \\wedge A| = |A| for some k in {2,...,|A|-2}. This result answers a question of Diderrich. Our proof relies on an elementary property of proper edge-colourings of the complete graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-26T18:50:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "finite subset",
      "distinct elements",
      "complete graph",
      "result answers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1961G"
    }
  }
}