{
  "id": "1702.02936",
  "version": "v1",
  "published": "2017-02-09T18:45:18.000Z",
  "updated": "2017-02-09T18:45:18.000Z",
  "title": "A bijective proof of Macdonald's reduced word formula",
  "authors": [
    "Sara C. Billey",
    "Alexander E. Holroyd",
    "Benjamin Young"
  ],
  "comment": "39 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a bijective proof of Macdonald's reduced word identity using pipe dreams and Little's bumping algorithm. This proof extends to a principal specialization due to Fomin and Stanley. Such a proof has been sought for over 20 years. Our bijective tools also allow us to solve a problem posed by Fomin and Kirillov from 1997 using work of Wachs, Lenart, Serrano and Stump. These results extend earlier work by the third author on a Markov process for reduced words of the longest permutation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-09T18:45:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19"
    ],
    "keywords": [
      "macdonalds reduced word formula",
      "bijective proof",
      "results extend earlier work",
      "macdonalds reduced word identity",
      "longest permutation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}