{
  "id": "1108.1041",
  "version": "v1",
  "published": "2011-08-04T10:41:33.000Z",
  "updated": "2011-08-04T10:41:33.000Z",
  "title": "Some formulas for numbers of line segments and lines in a rectangular grid",
  "authors": [
    "Pentti Haukkanen",
    "Jorma K. Merikoski"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We present a formula for the number of line segments connecting q+1 points of an n_1 x...x n_k rectangular grid. As corollaries, we obtain formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case k=2 is so generalized. We also present recursive formulas for these numbers assuming k=2, n_1=n_2. The well-known case q=2 is so generalized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-04T10:41:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A99",
      "11B37",
      "11P21"
    ],
    "keywords": [
      "rectangular grid",
      "well-known case",
      "line segments connecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1041H"
    }
  }
}