{
  "id": "math/0504230",
  "version": "v1",
  "published": "2005-04-11T21:39:12.000Z",
  "updated": "2005-04-11T21:39:12.000Z",
  "title": "Ehrhart-Macdonald reciprocity extended",
  "authors": [
    "Matthias Beck",
    "Richard Ehrenborg"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A similar counting function and reciprocity law exists for the sum of all solid angles at integer points in dilates of P. We derive a unifying generalization of these reciprocity theorems which follows in a natural way from Brion's Theorem on conic decompositions of polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-11T21:39:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C07",
      "05A15"
    ],
    "keywords": [
      "integer points",
      "counting function",
      "ehrhart-macdonald reciprocity law",
      "brions theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4230B"
    }
  }
}