{
  "id": "2404.04246",
  "version": "v1",
  "published": "2024-04-05T17:52:05.000Z",
  "updated": "2024-04-05T17:52:05.000Z",
  "title": "On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials",
  "authors": [
    "Grant T. Barkley",
    "Christian Gaetz"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti's conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-05T17:52:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic kazhdan-lusztig polynomials",
      "combinatorial invariance conjecture",
      "lower bruhat intervals",
      "parabolic analog",
      "parabolic conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}