{
  "id": "1101.0410",
  "version": "v1",
  "published": "2011-01-02T15:25:39.000Z",
  "updated": "2011-01-02T15:25:39.000Z",
  "title": "Equivalence Classes of Full-Dimensional 0/1-Polytopes with Many Vertices",
  "authors": [
    "William Y. C. Chen",
    "Peter L. Guo"
  ],
  "comment": "34 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "Let $Q_n$ denote the $n$-dimensional hypercube with the vertex set $V_n=\\{0,1}^n$. A 0/1-polytope of $Q_n$ is a convex hull of a subset of $V_n$. This paper is concerned with the enumeration of equivalence classes of full-dimensional 0/1-polytopes under the symmetries of the hypercube. With the aid of a computer program, Aichholzer completed the enumeration of equivalence classes of full-dimensional 0/1-polytopes for $Q_4$, $Q_5$, and those of $Q_6$ up to 12 vertices. In this paper, we present a method to compute the number of equivalence classes of full-dimensional 0/1-polytopes of $Q_n$ with more than $2^{n-3}$ vertices. As an application, we finish the counting of equivalence classes of full-dimensional 0/1-polytopes of $Q_6$ with more than 12 vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-02T15:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "52A20",
      "52B12",
      "05C25"
    ],
    "keywords": [
      "equivalence classes",
      "full-dimensional",
      "computer program",
      "enumeration",
      "dimensional hypercube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}