{
  "id": "math/0310142",
  "version": "v1",
  "published": "2003-10-10T09:50:11.000Z",
  "updated": "2003-10-10T09:50:11.000Z",
  "title": "Lower bounds for simplicial covers and triangulations of cubes",
  "authors": [
    "Adam Bliss",
    "Francis Edward Su"
  ],
  "comment": "17 pages, related work at http://www.math.hmc.edu/~su/papers.html",
  "journal": "Discrete Comput. Geom. 33 (2005), 669--686",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "We show that the size of a minimal simplicial cover of a polytope $P$ is a lower bound for the size of a minimal triangulation of $P$, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their exterior faces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-10T09:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B11",
      "52B12",
      "52B05"
    ],
    "keywords": [
      "lower bound",
      "exterior faces",
      "minimal simplicial cover",
      "study minimal triangulations",
      "extra vertices"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10142B"
    }
  }
}