{
  "id": "math/0702717",
  "version": "v2",
  "published": "2007-02-23T21:46:13.000Z",
  "updated": "2007-03-22T15:14:53.000Z",
  "title": "Topological obstructions for vertex numbers of Minkowski sums",
  "authors": [
    "Raman Sanyal"
  ],
  "comment": "13 pages, 2 figures; Improved exposition and less typos. Construction/example and remarks added",
  "journal": "J. Combin. Theory Ser. A 116 (2009), no. 1, 168-179",
  "doi": "10.1016/j.jcta.2008.05.009",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "We show that for polytopes P_1, P_2, ..., P_r \\subset \\R^d, each having n_i \\ge d+1 vertices, the Minkowski sum P_1 + P_2 + ... + P_r cannot achieve the maximum of \\prod_i n_i vertices if r \\ge d. This complements a recent result of Fukuda & Weibel (2006), who show that this is possible for up to d-1 summands. The result is obtained by combining methods from discrete geometry (Gale transforms) and topological combinatorics (van Kampen--type obstructions) as developed in R\\\"{o}rig, Sanyal, and Ziegler (2007).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-22T15:14:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05"
    ],
    "keywords": [
      "minkowski sum",
      "vertex numbers",
      "topological obstructions",
      "van kampen-type obstructions",
      "discrete geometry"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2717S"
    }
  }
}