Carries, shuffling, and symmetric functions

Details Carries, shuffling, and symmetric functions Carries, shuffling, and symmetric functions

2009-02-02

arxiv.org/abs/0902.0179v1

Mathematics

Combinatorics

23 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Carries, shuffling, and symmetric functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Carries, shuffling, and symmetric functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Carries, shuffling, and symmetric functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159009