{
  "id": "1708.06292",
  "version": "v1",
  "published": "2017-08-21T15:41:48.000Z",
  "updated": "2017-08-21T15:41:48.000Z",
  "title": "A refined count of Coxeter element factorizations",
  "authors": [
    "Elise delMas",
    "Thomas Hameister",
    "Victor Reiner"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "For well-generated complex reflection groups, Chapuy and Stump gave a simple product for a generating function counting reflection factorizations of a Coxeter element by their length. This is refined here to record the number of reflections used from each orbit of hyperplanes. The proof is case-by-case via the classification of well-generated groups. It implies a new expression for the Coxeter number, expressed via data coming from a hyperplane orbit; a case-free proof of this due to J. Michel is included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-21T15:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "20F55"
    ],
    "keywords": [
      "coxeter element factorizations",
      "refined count",
      "generating function counting reflection factorizations",
      "well-generated complex reflection groups",
      "hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}