{
  "id": "math/0702786",
  "version": "v1",
  "published": "2007-02-26T15:29:00.000Z",
  "updated": "2007-02-26T15:29:00.000Z",
  "title": "Convex hulls of polyominoes",
  "authors": [
    "Sascha Kurz"
  ],
  "comment": "13 pages, 10 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of n unit hypercubes in the d-dimensional Euclidean space. For d=2 we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-26T15:29:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B50",
      "05D99",
      "52C99"
    ],
    "keywords": [
      "convex hull",
      "d-dimensional euclidean space",
      "facet-to-facet connected system",
      "maximum volume",
      "unit hypercubes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2786K"
    }
  }
}