{
  "id": "1006.5928",
  "version": "v1",
  "published": "2010-06-30T17:18:14.000Z",
  "updated": "2010-06-30T17:18:14.000Z",
  "title": "The flag polynomial of the Minkowski sum of simplices",
  "authors": [
    "Geir Agnarsson"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a polytope we define the {\\em flag polynomial}, a polynomial in commuting variables related to the well-known flag vector and describe how to express the the flag polynomial of the Minkowski sum of $k$ standard simplices in a direct and canonical way in terms of the {\\em $k$-th master polytope} $P(k)$ where $k\\in\\nats$. The flag polynomial facilitates many direct computations. To demonstrate this we provide two examples; we first derive a formula for the $f$-polynomial and the maximum number of $d$-dimensional faces of the Minkowski sum of two simplices. We then compute the maximum discrepancy between the number of $(0,d)$-chains of faces of a Minkowski sum of two simplices and the number of such chains of faces of a simple polytope of the same dimension and on the same number of vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-30T17:18:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16",
      "52B05",
      "52B11"
    ],
    "keywords": [
      "minkowski sum",
      "th master polytope",
      "flag polynomial facilitates",
      "well-known flag vector",
      "direct computations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.5928A"
    }
  }
}