{
  "id": "math/0507186",
  "version": "v2",
  "published": "2005-07-08T19:45:22.000Z",
  "updated": "2005-12-14T21:52:41.000Z",
  "title": "Clusters, Coxeter-sortable elements and noncrossing partitions",
  "authors": [
    "Nathan Reading"
  ],
  "comment": "Minor changes in exposition, including: More precise statement in Remark 6.8; Added Remark 6.9, an observation which is helpful in the sequel (math.CO/0512339); Updated textual references to the sequel and to a paper in preparation (with D. Speyer). 28 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-12-14T21:52:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "05E15",
      "05A15"
    ],
    "keywords": [
      "noncrossing partitions",
      "coxeter group",
      "inversion sets",
      "bijective proofs",
      "characterize coxeter-sortable elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7186R"
    }
  }
}