{
  "id": "math/9712257",
  "version": "v1",
  "published": "1997-12-17T16:09:52.000Z",
  "updated": "1997-12-17T16:09:52.000Z",
  "title": "Fiber polytopes for the projections between cyclic polytopes",
  "authors": [
    "C. A. Athanasiadis",
    "J. A. De Loera",
    "V. Reiner",
    "F. Santos"
  ],
  "comment": "28 pages with 1 postscript figure",
  "journal": "European J. Combin. 21:1 (2000), 19-47",
  "doi": "10.1006/eujc.1999.0319",
  "categories": [
    "math.CO"
  ],
  "abstract": "The cyclic polytope $C(n,d)$ is the convex hull of any $n$ points on the moment curve ${(t,t^2,...,t^d):t \\in \\reals}$ in $\\reals^d$. For $d' >d$, we consider the fiber polytope (in the sense of Billera and Sturmfels) associated to the natural projection of cyclic polytopes $\\pi: C(n,d') \\to C(n,d)$ which \"forgets\" the last $d'-d$ coordinates. It is known that this fiber polytope has face lattice indexed by the coherent polytopal subdivisions of $C(n,d)$ which are induced by the map $\\pi$. Our main result characterizes the triples $(n,d,d')$ for which the fiber polytope is canonical in either of the following two senses: - all polytopal subdivisions induced by $\\pi$ are coherent, - the structure of the fiber polytope does not depend upon the choice of points on the moment curve. We also discuss a new instance with a positive answer to the Generalized Baues Problem, namely that of a projection $\\pi:P\\to Q$ where $Q$ has only regular subdivisions and $P$ has two more vertices than its dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-12-17T16:09:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "52B12",
      "52B35"
    ],
    "keywords": [
      "fiber polytope",
      "cyclic polytope",
      "moment curve",
      "coherent polytopal subdivisions",
      "main result characterizes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math.....12257A"
    }
  }
}