Carries, shuffling, and symmetric functions
Combinatorics
2009-02-03 v1 Probability
Abstract
The "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.
Keywords
Cite
@article{arxiv.0902.0179,
title = {Carries, shuffling, and symmetric functions},
author = {Persi Diaconis and Jason Fulman},
journal= {arXiv preprint arXiv:0902.0179},
year = {2009}
}
Comments
23 pages