The combinatorics of biased riffle shuffles
A generalization of the riffle shuffle as introduced by Gilbert, Shannon and Reeds (GSR) is discussed. This generalization was already introduced before but had still to be analyzed. The author generalizes several of the known results on the GSR-shuffles. He gives bounds on the time the new shuffles need to converge to the uniform distribution. Next the statistics on the structure (cycles, inversions and descents) of the permutations evolving from biased riffle shuffles are investigated.
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