{
  "id": "1508.05524",
  "version": "v1",
  "published": "2015-08-22T16:37:19.000Z",
  "updated": "2015-08-22T16:37:19.000Z",
  "title": "Sets with few differences in abelian groups",
  "authors": [
    "Mitchell Lee"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $(G, +)$ be an abelian group. In 2004, Eliahou and Kervaire found an explicit formula for the smallest possible cardinality of the sumset $A+A$, where $A \\subseteq G$ has fixed cardinality $r$. We consider instead the smallest possible cardinality of the difference set $A-A$, which is always greater than or equal to the smallest possible cardinality of $A+A$ and can be strictly greater. We conjecture a formula for this quantity, and prove the conjecture in the case that $G$ is a cyclic group or a vector space over a finite field. This resolves a conjecture of Bajnok and Matzke on signed sumsets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-22T16:37:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "conjecture",
      "finite field",
      "explicit formula",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805524L"
    }
  }
}