{
  "id": "math/0602293",
  "version": "v1",
  "published": "2006-02-14T09:31:19.000Z",
  "updated": "2006-02-14T09:31:19.000Z",
  "title": "h-vectors of generalized associahedra and non-crossing partitions",
  "authors": [
    "Christos A. Athanasiadis",
    "Thomas Brady",
    "Jon McCammond",
    "Colum Watt"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "A case-free proof is given that the entries of the $h$-vector of the cluster complex $\\Delta (\\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\\Phi$, count elements of the lattice $\\nc$ of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\\Delta (\\Phi)$ are provided. The proof utilizes the appearance of the complex $\\Delta (\\Phi)$ in the context of the lattice $\\nc$, in recent work of two of the authors, as well as an explicit shelling of $\\Delta (\\Phi)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-14T09:31:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "generalized associahedra",
      "non-crossing partitions",
      "finite root system",
      "proof utilizes",
      "case-free proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2293A"
    }
  }
}