9 Carries , Shuffling , and Symmetric Functions
نویسنده
چکیده
The “carries” when n random numbers are added base b form a Markov chain with an “amazing” transition matrix determined by Holte [24]. This same Markov chain occurs in following the number of descents or rising sequences when n cards are repeatedly riffle shuffled. We give generating and symmetric function proofs and determine the rate of convergence of this Markov chain to stationarity. Similar results are given for type B shuffles. We also develop connections with Gaussian autoregressive processes and the Veronese mapping of commutative algebra.
منابع مشابه
Carries, shuffling, and symmetric functions
Article history: Received 1 February 2009 Accepted 11 February 2009 Available online 15 April 2009 MSC: 60C05 60J10 05E05
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