1997/12/09 by Jason Fulman, Fulman, Jason
Computer Science · Mathematics · #05A15 #60C05 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05A15 #msc:60C05
paper · pdf · doi:10.48550/arxiv.math/9712240
11 pages
arxiv created 1997/12/09 · openalex publication_date 1997/12/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.