{
  "id": "0804.4716",
  "version": "v1",
  "published": "2008-04-30T13:15:00.000Z",
  "updated": "2008-04-30T13:15:00.000Z",
  "title": "On Combinatorial Formulas for Macdonald Polynomials",
  "authors": [
    "Cristian Lenart"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram-Yip formula compresses to a new formula, which is similar to the Haglund-Haiman-Loehr one but contains considerably fewer terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-30T13:15:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "33D52"
    ],
    "keywords": [
      "macdonald polynomials",
      "combinatorial formula",
      "contains considerably fewer terms",
      "ram-yip formula compresses",
      "littelmann path model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4716L"
    }
  }
}