{
  "id": "1211.4305",
  "version": "v1",
  "published": "2012-11-19T05:28:46.000Z",
  "updated": "2012-11-19T05:28:46.000Z",
  "title": "Inequalities on Bruhat graphs, R- and Kazhdan-Lusztig polynomials",
  "authors": [
    "Masato Kobayashi"
  ],
  "comment": "16 pages",
  "journal": "Journal of Combinatorial Series A 120 (2013) no.2, 470--482",
  "categories": [
    "math.CO"
  ],
  "abstract": "From a combinatorial perspective, we establish three inequalities on coefficients of $R$- and Kazhdan-Lusztig polynomials for crystallographic Coxeter groups: (1) Nonnegativity of $(q-1)$-coefficients of $R$-polynomials, (2) a new criterion of rational singularities of Bruhat intervals by sum of quadratic coefficients of $R$-polynomials, (3) existence of a certain strict inequality (coefficientwise) of Kazhdan-Lusztig polynomials. Our main idea is to understand Deodhar's inequality in a connection with a sum of $R$-polynomials and edges of Bruhat graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-19T05:28:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "51F15"
    ],
    "keywords": [
      "kazhdan-lusztig polynomials",
      "bruhat graphs",
      "understand deodhars inequality",
      "crystallographic coxeter groups",
      "bruhat intervals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4305K"
    }
  }
}