{
  "id": "1511.03743",
  "version": "v1",
  "published": "2015-11-12T01:07:54.000Z",
  "updated": "2015-11-12T01:07:54.000Z",
  "title": "Sums of sets of lattice points and unimodular coverings of polytopes",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "If $P$ is a lattice polytope (that is, the convex hull of a finite set of lattice points in $\\mathbf{R}^n$), then every sum of $h$ lattice points in $P$ is a lattice point in the $h$-fold sumset $hP$. However, a lattice point in the $h$-fold sumset $hP$ is not necessarily the sum of $h$ lattice points in $P$. It is proved that if the polytope $P$ is a union of unimodular simplices, then every lattice point in the $h$-fold sumset $hP$ is the sum of $h$ lattice points in $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-12T01:07:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "11P21",
      "52A10",
      "52B20",
      "52C05"
    ],
    "keywords": [
      "lattice point",
      "unimodular coverings",
      "fold sumset",
      "lattice polytope",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151103743N"
    }
  }
}