{
  "id": "math/0005052",
  "version": "v1",
  "published": "2000-05-05T16:38:53.000Z",
  "updated": "2000-05-05T16:38:53.000Z",
  "title": "Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations",
  "authors": [
    "Sara C. Billey",
    "Gregory S. Warrington"
  ],
  "comment": "24 pages, 18 figures, AMS-LaTeX",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a combinatorial formula for the Kazhdan-Lusztig polynomials $P_{x,w}$ in the symmetric group when $w$ is a 321-hexagon-avoiding permutation. Our formula, which depends on a combinatorial framework developed by Deodhar, can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for $w$. We also show that $w$ being 321-hexagon-avoiding is equivalent to several other conditions, such as the Bott-Samelson resolution of the Schubert variety $X_w$ being small. We conclude with a simple method for completely determining the singular locus of $X_w$ when $w$ is 321-hexagon-avoiding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-05-05T16:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "20F55",
      "32S45",
      "14M15"
    ],
    "keywords": [
      "kazhdan-lusztig polynomials",
      "permutation",
      "symmetric group",
      "singular locus",
      "simple statistic"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......5052B"
    }
  }
}