{
  "id": "1812.06266",
  "version": "v1",
  "published": "2018-12-15T10:31:55.000Z",
  "updated": "2018-12-15T10:31:55.000Z",
  "title": "Bruhat order and graph structures of lower intervals in Coxeter groups",
  "authors": [
    "Masato Kobayashi"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded posets, and two-sided quotients altogether. For this purpose, we introduce some new ideas, quotient lower intervals and quotient Bruhat graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-15T10:31:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "51F15"
    ],
    "keywords": [
      "coxeter group",
      "graph structures",
      "bruhat order",
      "quotient lower intervals",
      "lower bruhat interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}