{
  "id": "0906.4768",
  "version": "v4",
  "published": "2009-06-25T18:32:27.000Z",
  "updated": "2020-06-01T18:13:18.000Z",
  "title": "Diameter of reduced words",
  "authors": [
    "Victor Reiner",
    "Yuval Roichman"
  ],
  "comment": "Version 4 points out a gap in the proof of Theorem 4.9, filled in work of T. McConville (arXiv:1411.1305)",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-07T22:49:02.000Z",
      "comment": "Version to appear in Trans. Amer. Math. Soc",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2020-06-01T18:13:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20F05"
    ],
    "keywords": [
      "reduced words",
      "finite reflection groups",
      "longest element",
      "supersolvable hyperplane arrangements",
      "general theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4768R"
    }
  }
}