{
  "id": "1009.4918",
  "version": "v2",
  "published": "2010-09-24T19:42:29.000Z",
  "updated": "2010-10-22T15:25:52.000Z",
  "title": "Bounding reflection length in an affine Coxeter group",
  "authors": [
    "Jon McCammond",
    "T. Kyle Petersen"
  ],
  "comment": "10 pages. Replaces earlier posting by second author. Paper is substantially reorganized and includes stronger results, including sharpness of the upper bound",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "In any Coxeter group, the conjugates of elements in the standard minimal generating set are called reflections and the minimal number of reflections needed to factor a particular element is called its reflection length. In this article we prove that the reflection length function on an affine Coxeter group has a uniform upper bound. More precisely we prove that the reflection length function on an affine Coxeter group that naturally acts faithfully and cocompactly on $\\R^n$ is bounded above by $2n$ and we also show that this bound is optimal. Conjecturally, spherical and affine Coxeter groups are the only Coxeter groups with a uniform bound on reflection length.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-22T15:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "affine coxeter group",
      "bounding reflection length",
      "reflection length function",
      "standard minimal generating set",
      "uniform upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4918M"
    }
  }
}