C.Y. Amy Pang - A Hopf-power Markov chain on compositions

dmtcs:2316 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2316
A Hopf-power Markov chain on compositionsArticle

Authors: C.Y. Amy Pang ORCID1

  • 1 Department of Mathematics [Stanford]

In a recent paper, Diaconis, Ram and I constructed Markov chains using the coproduct-then-product map of a combinatorial Hopf algebra. We presented an algorithm for diagonalising a large class of these "Hopf-power chains", including the Gilbert-Shannon-Reeds model of riffle-shuffling of a deck of cards and a rock-breaking model. A very restrictive condition from that paper is removed in my thesis, and this extended abstract focuses on one application of the improved theory. Here, I use a new technique of lumping Hopf-power chains to show that the Hopf-power chain on the algebra of quasisymmetric functions is the induced chain on descent sets under riffle-shuffling. Moreover, I relate its right and left eigenfunctions to Garsia-Reutenauer idempotents and ribbon characters respectively, from which I recover an analogous result of Diaconis and Fulman (2012) concerning the number of descents under riffle-shuffling.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Quasisymmetric functions,riffle shuffling,descent set,combinatorial Hopf algebras,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

1 Document citing this article

Consultation statistics

This page has been seen 283 times.
This article's PDF has been downloaded 311 times.