{
  "id": "0709.4241",
  "version": "v3",
  "published": "2007-09-26T19:42:37.000Z",
  "updated": "2008-04-17T18:20:33.000Z",
  "title": "Permutahedra and generalized associahedra",
  "authors": [
    "Christophe Hohlweg",
    "Carsten Lange",
    "Hugh Thomas"
  ],
  "comment": "27 pages, 10 figures; v3: 31 pages, 10 figures, Section 3 is rewritten, corrected typos, and updated references",
  "journal": "Advances in Math., 226 (2011), pp.608-640",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a finite Coxeter system $(W,S)$ and a Coxeter element $c$, we construct a simple polytope whose outer normal fan is N. Reading's Cambrian fan $F_c$, settling a conjecture of Reading that this is possible. We call this polytope the $c$-generalized associahedron. Our approach generalizes Loday's realization of the associahedron (a type $A$ $c$-generalized associahedron whose outer normal fan is not the cluster fan but a coarsening of the Coxeter fan arising from the Tamari lattice) to any finite Coxeter group. A crucial role in the construction is played by the $c$-singleton cones, the cones in the $c$-Cambrian fan which consist of a single maximal cone from the Coxeter fan. Moreover, if $W$ is a Weyl group and the vertices of the permutahedron are chosen in a lattice associated to $W$, then we show that our realizations have integer coordinates in this lattice.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-17T18:20:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "06B99",
      "52B11",
      "05E99"
    ],
    "keywords": [
      "generalized associahedron",
      "outer normal fan",
      "permutahedron",
      "approach generalizes lodays realization",
      "coxeter fan"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.4241H"
    }
  }
}