{
  "id": "math/9704217",
  "version": "v1",
  "published": "1997-04-08T00:00:00.000Z",
  "updated": "1997-04-08T00:00:00.000Z",
  "title": "On Subdivision Posets of Cyclic Polytopes",
  "authors": [
    "Paul H. Edelman",
    "Jörg Rambau",
    "Victor Reiner"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic $d$ polytope with $n$ vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension $n-d-3$. Moreover, we resolve positively a new special case of the \\emph{Generalized Baues Problem}: The Baues poset of all polytopal decompositions of a cyclic polytope of dimension $d \\leq 3$ has the homotopy type of a sphere of dimension $n-d-2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-04-08T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic polytope",
      "subdivision posets",
      "homotopy type",
      "higher stasheff-tamari orders",
      "related poset structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......4217E"
    }
  }
}