Carries, shuffling, and symmetric functions

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dc.creatorDiaconis, Persi
dc.creatorFulman, Jason
dc.date2009-02-02
dc.date.accessioned2026-07-07T12:36:54Z
dc.date.available2026-07-07T12:36:54Z
dc.descriptionThe "carries" when n random numbers are added base b form a Markov chain with an "amazing" transition matrix determined by Holte. 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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0902.0179
dc.identifierhttp://arxiv.org/abs/0902.0179
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218257
dc.subjectCombinatorics
dc.subjectProbability
dc.subject60C05, 60J10, 05E05
dc.titleCarries, shuffling, and symmetric functions
dc.typetext

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