{
  "id": "1506.02331",
  "version": "v1",
  "published": "2015-06-08T00:47:16.000Z",
  "updated": "2015-06-08T00:47:16.000Z",
  "title": "On the span of lattice points in a parallelepiped",
  "authors": [
    "Marcel Celaya"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO",
    "math.AG",
    "math.NT"
  ],
  "abstract": "We find a good characterization for the following problem: Given an integral row vector $c=(c_{1}\\ldots,c_{n})$ where each $c_{i}\\in\\{-1,0,1\\}$ and a lattice $\\Lambda\\subset\\mathbf{R}^{n}$ which contains the integer lattice $\\mathbf{Z}^{n}$, do all lattice points of $\\Lambda$ in the half-open unit cube $[0,1)^{n}$ lie on the hyperplane $\\{x:cx=0\\}$? The result is a direct generalization of the well-known Terminal Lemma of Reid, which in turn is based upon earlier work of Morrison and Stevens on the classification of terminal quotient singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-08T00:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52B05",
      "11M20"
    ],
    "keywords": [
      "lattice points",
      "integral row vector",
      "half-open unit cube",
      "well-known terminal lemma",
      "terminal quotient singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}