{
  "id": "math/0501100",
  "version": "v3",
  "published": "2005-01-07T13:15:33.000Z",
  "updated": "2005-12-12T10:11:15.000Z",
  "title": "Polygon dissections and some generalizations of cluster complexes",
  "authors": [
    "Eleni Tzanaki"
  ],
  "comment": "9 pages, 3 figures, the type D case has been removed, some corrections on the proof of Theorem 3.1 have been made. To appear in JCTA",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $W$ be a Weyl group corresponding to the root system $A_{n-1}$ or $B_n$. We define a simplicial complex $ \\Delta^m_W $ in terms of polygon dissections for such a group and any positive integer $m$. For $ m=1 $, $ \\Delta^m_W$ is isomorphic to the cluster complex corresponding to $ W $, defined in \\cite{FZ}. We enumerate the faces of $ \\Delta^m_W $ and show that the entries of its $h$-vector are given by the generalized Narayana numbers $ N^m_W(i) $, defined in \\cite{Atha3}. We also prove that for any $ m \\geq 1$ the complex $ \\Delta^m_W $ is shellable and hence Cohen-Macaulay.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-12-12T10:11:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polygon dissections",
      "cluster complexes",
      "generalizations",
      "root system",
      "weyl group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1100T"
    }
  }
}