{
  "id": "math/0301104",
  "version": "v2",
  "published": "2003-01-10T17:32:41.000Z",
  "updated": "2003-06-17T10:31:44.000Z",
  "title": "Freely braided elements in Coxeter groups",
  "authors": [
    "R. M. Green",
    "J. Losonczy"
  ],
  "comment": "18 pages, AMSTeX. Results renumbered to agree with published version",
  "journal": "Annals of Combinatorics 6 (2002), 337-348",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We introduce a notion of \"freely braided element\" for simply laced Coxeter groups. We show that an arbitrary group element $w$ has at most $2^{N(w)}$ commutation classes of reduced expressions, where $N(w)$ is a certain statistic defined in terms of the positive roots made negative by $w$. This bound is achieved if $w$ is freely braided. In the type $A$ setting, we show that the bound is achieved only for freely braided $w$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-06-17T10:31:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "freely braided element",
      "arbitrary group element",
      "simply laced coxeter groups",
      "commutation classes",
      "reduced expressions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1104G"
    }
  }
}