{
  "id": "1108.1913",
  "version": "v1",
  "published": "2011-08-09T12:50:11.000Z",
  "updated": "2011-08-09T12:50:11.000Z",
  "title": "Conditions to Extend Partial Latin Rectangles",
  "authors": [
    "Serge C. Ballif"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1974 Allan Cruse provided necessary and sufficient conditions to extend an $r\\times s$ partial latin rectangle consisting of $t$ distinct symbols to a latin square of order $n$. Here we provide some generalizations and consequences of this result. Our results are obtained via an alternative proof of Cruse's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-09T12:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "extend partial latin rectangles",
      "sufficient conditions",
      "partial latin rectangle consisting",
      "allan cruse",
      "distinct symbols"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1913B"
    }
  }
}