{
  "id": "1612.03764",
  "version": "v1",
  "published": "2016-12-12T16:16:44.000Z",
  "updated": "2016-12-12T16:16:44.000Z",
  "title": "Generating series of cyclically fully commutative elements is rational",
  "authors": [
    "Mathias Pétréolle"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the generating function of cyclically fully commutative elements in Coxeter groups, which are elements such that any cyclic shift of theirs reduced decompositions remains a reduced expression of a fully commutative element. By designing a finite state automaton recognizing reduced expressions of cyclically fully commutative elements, we can show that the aforementioned generating series is always rational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T16:16:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclically fully commutative elements",
      "generating series",
      "finite state automaton",
      "state automaton recognizing reduced expressions",
      "coxeter groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}