The combinatorics of biased riffle shuffles
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Publication:1297761
DOI10.1007/PL00009814zbMATH Open0932.60007arXivmath/9712240OpenAlexW2036533844MaRDI QIDQ1297761
Author name not available (Why is that?)
Publication date: 14 September 1999
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/9712240
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