{
  "id": "0704.3067",
  "version": "v1",
  "published": "2007-04-23T22:06:24.000Z",
  "updated": "2007-04-23T22:06:24.000Z",
  "title": "Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations",
  "authors": [
    "Brant C. Jones"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We provide a non-recursive description for the bounded admissible sets of masks used by Deodhar's algorithm to calculate the Kazhdan--Lusztig polynomials $P_{x,w}(q)$ of type $A$, in the case when $w$ is hexagon avoiding and maximally clustered. This yields a combinatorial description of the Kazhdan--Lusztig basis elements of the Hecke algebra associated to such permutations $w$. The maximally-clustered hexagon-avoiding elements are characterized by avoiding the seven classical permutation patterns $\\{3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234\\}$. We also briefly discuss the application of heaps to permutation pattern characterization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-23T22:06:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "kazhdan-lusztig polynomials",
      "maximally-clustered hexagon-avoiding permutations",
      "seven classical permutation patterns",
      "kazhdan-lusztig basis elements",
      "permutation pattern characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3067J"
    }
  }
}