{
  "id": "1112.0856",
  "version": "v2",
  "published": "2011-12-05T08:24:41.000Z",
  "updated": "2013-03-07T20:26:45.000Z",
  "title": "The absolute order of a permutation representation of a Coxeter group",
  "authors": [
    "Christos A. Athanasiadis",
    "Yuval Roichman"
  ],
  "comment": "23 pages, 1 figure, revised version to be published in J. Algebraic Combinatorics",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "A permutation representation of a Coxeter group $W$ naturally defines an absolute order. This family of partial orders (which includes the absolute order on $W$) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on $W$ are investigated when $W$ is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of $W$ is defined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-07T20:26:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "20F55"
    ],
    "keywords": [
      "permutation representation",
      "coxeter group",
      "associated rank generating polynomial divides",
      "symmetric group action",
      "partial orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0856A"
    }
  }
}