{
  "id": "1105.5889",
  "version": "v2",
  "published": "2011-05-30T07:43:58.000Z",
  "updated": "2011-09-02T19:43:25.000Z",
  "title": "Bases of minimal vectors in lattices, III",
  "authors": [
    "Jacques Martinet",
    "Achill Schürmann"
  ],
  "comment": "16 pages, contains minor changes suggested by referee",
  "journal": "International Journal of Number Theory, 8 (2012), 551-564",
  "doi": "10.1142/S1793042112500303",
  "categories": [
    "math.NT",
    "math.MG"
  ],
  "abstract": "We prove that all Euclidean lattices of dimension $n\\le 9$ which are generated by their minimal vectors, also possess a basis of minimal vectors. By providing a new counterexample, we show that this is not the case for all dimensions $n\\ge 10$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-02T19:43:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H55"
    ],
    "keywords": [
      "minimal vectors",
      "euclidean lattices",
      "counterexample"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5889M"
    }
  }
}