{
  "id": "math/0512339",
  "version": "v1",
  "published": "2005-12-14T19:59:59.000Z",
  "updated": "2005-12-14T19:59:59.000Z",
  "title": "Sortable elements and Cambrian lattices",
  "authors": [
    "Nathan Reading"
  ],
  "comment": "23 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-14T19:59:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "06B10"
    ],
    "keywords": [
      "cambrian lattice",
      "weak order",
      "coxeter-sortable elements",
      "finite coxeter group",
      "minimal congruence-class representatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12339R"
    }
  }
}