Carries, shuffling, and symmetric functions (Q1030692)

The authors discuss the carries process, riffle shuffling and finally the connection. They use generating functions and symmetric function theory to explain a surprising coincidence: When \(n\) long integers are added (base \(b\)), the distribution of ``carries'' is the same as distribution of descents when \(n\) cards are repeatedly riffled shuffled. The explanation yields a sharp analysis of convergence to stationary of the associated Markov chains. A similar analysis goes through for type B shuffles. They also develop connections with Gaussian autoregressive processes and Veronese mapping of commutative algebra.