{
  "id": "1304.3650",
  "version": "v3",
  "published": "2013-04-12T14:41:27.000Z",
  "updated": "2015-09-11T13:39:25.000Z",
  "title": "A note on a sumset in $\\mathbb{Z}_{2k}$",
  "authors": [
    "Octavio A. Agustín-Aquino"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A$ and $B$ be additive sets of $\\mathbb{Z}_{2k}$, where $A$ has cardinality $k$ and $B=v.\\complement A$ with $v\\in\\mathbb{Z}_{2k}^{\\times}$. In this note some bounds for the cardinality of $A+B$ are obtained, using four different approaches. We also prove that in a special case the bound is not sharp and we can recover the whole group as a sumset.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-09T08:15:52.000Z",
      "abstract": "Let $A$ and $B$ be additive sets of $\\mathbb{Z}_{2k}$, where $A$ has cardinality $k$ and $B=v.\\complement A$ with $v\\in\\mathbb{Z}_{2k}^{\\times}$. In this note some bounds for the cardinality of $A+B$ are obtained, using four different approaches.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-09-11T13:39:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "11L07"
    ],
    "keywords": [
      "cardinality",
      "additive sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3650A"
    }
  }
}