{
  "id": "1612.09443",
  "version": "v1",
  "published": "2016-12-30T10:16:22.000Z",
  "updated": "2016-12-30T10:16:22.000Z",
  "title": "Transversals in Latin arrays with many distinct symbols",
  "authors": [
    "Darcy Best",
    "Kevin Hendrey",
    "Ian M. Wanless",
    "Tim E. Wilson",
    "David R. Wood"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An array is row-Latin if no symbol is repeated within any row. An array is Latin if it and its transpose are both row-Latin. A transversal in an $n\\times n$ array is a selection of $n$ different symbols from different rows and different columns. We prove that every $n \\times n$ Latin array containing at least $(2-\\sqrt{2}) n^2$ distinct symbols has a transversal. Also, every $n \\times n$ row-Latin array containing at least $\\frac14(5-\\sqrt{5})n^2$ distinct symbols has a transversal. Finally, we show by computation that every Latin array of order $7$ has a transversal, and we describe all smaller Latin arrays that have no transversal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-30T10:16:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "distinct symbols",
      "transversal",
      "smaller latin arrays",
      "row-latin array containing",
      "computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}