{
  "id": "1306.2387",
  "version": "v1",
  "published": "2013-06-11T00:12:08.000Z",
  "updated": "2013-06-11T00:12:08.000Z",
  "title": "The number of lines in a matroid with no $U_{2,n}$-minor",
  "authors": [
    "Jim Geelen",
    "Peter Nelson"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that, if $q$ is a prime power at most 5, then every rank-$r$ matroid with no $U_{2,q+2}$-minor has no more lines than a rank-$r$ projective geometry over GF$(q)$. We also give examples showing that for every other prime power this bound does not hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-11T00:12:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime power",
      "projective geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2387G"
    }
  }
}