{
  "id": "math/0703435",
  "version": "v1",
  "published": "2007-03-14T20:18:49.000Z",
  "updated": "2007-03-14T20:18:49.000Z",
  "title": "On the maximally clustered elements of Coxeter groups",
  "authors": [
    "R. M. Green"
  ],
  "comment": "Approximately 18 pages, AMSTeX. One non-essential figure",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We continue the study of the maximally clustered elements for simply laced Coxeter groups which were recently introduced by Losonczy. Such elements include as a special case the freely braided elements of Losonczy and the author, which in turn constitute a superset of the $iji$-avoiding elements of Fan. Our main result is to classify the MC-finite Coxeter groups, namely those Coxeter groups having finitely many maximally clustered elements. Remarkably, any simply laced Coxeter group having finitely many $iji$-avoiding elements also turns out to be MC-finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-14T20:18:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "maximally clustered elements",
      "simply laced coxeter group",
      "avoiding elements",
      "mc-finite coxeter groups",
      "special case"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3435G"
    }
  }
}