{
  "id": "0710.3965",
  "version": "v2",
  "published": "2007-10-22T01:45:38.000Z",
  "updated": "2009-10-20T13:20:35.000Z",
  "title": "Quasisymmetric functions and Kazhdan-Lusztig polynomials",
  "authors": [
    "Louis J. Billera",
    "Francesco Brenti"
  ],
  "comment": "27 pages. Final version: definitions reorganized for clarity, added Example 4.6 and two citations. To appear in Israel Journal of Mathematics",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We associate a quasisymmetric function to any Bruhat interval in a general Coxeter group. This association can be seen to be a morphism of Hopf algebras to the subalgebra of all peak functions, leading to an extension of the cd-index of convex polytopes. We show how the Kazhdan-Lusztig polynomial of the Bruhat interval can be expressed in terms of this complete cd-index and otherwise explicit combinatorially defined polynomials. In particular, we obtain the simplest closed formula for the Kazhdan-Lusztig polynomials that holds in complete generality.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-20T13:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "05E99",
      "05E15"
    ],
    "keywords": [
      "kazhdan-lusztig polynomial",
      "quasisymmetric function",
      "bruhat interval",
      "general coxeter group",
      "simplest closed formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3965B"
    }
  }
}