{
  "id": "math/0510470",
  "version": "v4",
  "published": "2005-10-21T17:09:06.000Z",
  "updated": "2006-11-02T13:33:46.000Z",
  "title": "On f-vectors of Minkowski additions of convex polytopes",
  "authors": [
    "Komei Fukuda",
    "Christophe Weibel"
  ],
  "comment": "13 pages, submitted to Discrete & Computational Geometry",
  "journal": "Discrete & Computational Geometry, vol. 37 (2007), pp. 503-516",
  "doi": "10.1007/s00454-007-1310-2",
  "categories": [
    "math.CO"
  ],
  "abstract": "The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of face lattice of the sum in terms of the face lattice of a given perfectly centered polytope. Exact face counting formulas are then obtained for perfectly centered simplices and hypercubes. The second type of results concerns tight upper bounds for the f-vectors of Minkowski sums of several polytopes.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-11-02T13:33:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05"
    ],
    "keywords": [
      "convex polytopes",
      "minkowski additions",
      "minkowski sum",
      "results concerns tight upper bounds",
      "face lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10470F"
    }
  }
}