{
  "id": "math/0310120",
  "version": "v1",
  "published": "2003-10-08T18:06:52.000Z",
  "updated": "2003-10-08T18:06:52.000Z",
  "title": "Freely braided elements in Coxeter groups, II",
  "authors": [
    "R. M. Green",
    "J. Losonczy"
  ],
  "comment": "AMSTeX, approximately 19 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work (math.CO/0301104). A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that a simply laced Coxeter group has finitely many freely braided elements if and only if it has finitely many fully commutative elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-08T18:06:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "freely braided elements",
      "simply laced coxeter group",
      "commutation classes",
      "converse direction",
      "upper bound"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10120G"
    }
  }
}