{
  "id": "math/9712240",
  "version": "v1",
  "published": "1997-12-09T19:52:00.000Z",
  "updated": "1997-12-09T19:52:00.000Z",
  "title": "The combinatorics of biased riffle shuffles",
  "authors": [
    "Jason Fulman"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to converge to the uniform distribution; this matches lower bounds of Lalley. A careful version of a bijection of Gessel leads to a generating function for cycle structure after one of these shuffles and gives new results about descents in random permutations. Results are also obtained about the inversion and descent structure of a permutation after one of these shuffles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-12-09T19:52:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "60C05"
    ],
    "keywords": [
      "paper studies biased riffle shuffles",
      "combinatorics",
      "matches lower bounds",
      "random permutations",
      "cycle structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math.....12240F"
    }
  }
}