{
  "id": "1607.00563",
  "version": "v1",
  "published": "2016-07-02T21:20:14.000Z",
  "updated": "2016-07-02T21:20:14.000Z",
  "title": "On the additive bases problem in finite fields",
  "authors": [
    "Hamed Hatami",
    "Victoria de Quehen"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that if $G$ is an Abelian group and $A_1,\\ldots,A_k \\subseteq G$ satisfy $m A_i=G$ (the $m$-fold sumset), then $A_1+\\ldots+A_k=G$ provided that $k \\ge c_m \\log n$. This generalizes a result of Alon, Linial, and Meshulam [Additive bases of vector spaces over prime fields. J. Combin. Theory Ser. A, 57(2):203--210, 1991] regarding the so called additive bases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-02T21:20:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13"
    ],
    "keywords": [
      "additive bases problem",
      "finite fields",
      "fold sumset",
      "abelian group",
      "vector spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}