{
  "id": "0801.2987",
  "version": "v1",
  "published": "2008-01-18T22:56:29.000Z",
  "updated": "2008-01-18T22:56:29.000Z",
  "title": "The minimum rank problem over finite fields",
  "authors": [
    "Jason Grout"
  ],
  "comment": "23 pages, 5 figures, 1 Sage program",
  "categories": [
    "math.CO"
  ],
  "abstract": "The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characterization and polarities of projective geometries is explained. Using this connection, a few results in the minimum rank problem are derived by applying some known results from projective geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-18T22:56:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C75",
      "15A03",
      "05B25",
      "51E20"
    ],
    "keywords": [
      "minimum rank problem",
      "finite field",
      "projective geometry",
      "strong connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}