Trailing the Dovetail Shuffle to Its Lair by Dave
نویسنده
چکیده
We analyze the most commonly used method for shuffling cards. The main result is a simple expression for the chance of any arrangement after any number of shuffles. This is used to give sharp bounds on the approach to randomness: $ log, n + 0 shuffles are necessary and sufficient to mix up n cards. Key ingredients are the analysis of a card trick and the determination of the idempotents of a natural commutative subalgebra in the symmetric group algebra.
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Trailing the Dovetail Shuffle to its Lair
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Acknowledgement This paper was prompted in part by an inspiring course taught at Cornell by Persi Diaconis in the fall of 1996. For help and advice along the way we are grateful to Diaconis and to 29 References 1] D. Bayer and P. Diaconis, \Trailing the dovetail shuue to its lair," Ann. Appl. \Asymptotic analysis of a random walk on a hypercube with many dimensions," Random Struct. and Alg.
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تاریخ انتشار 2007