@inproceedings{757be9ad06fd4f87ab9b9f8011d30dac,
title = "A Hopf-power Markov chain on compositions",
abstract = "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.",
keywords = "Quasisymmetric functions, riffle shuffling, descent set, combinatorial Hopf algebras",
author = "Pang, {Amy C. Y.}",
year = "2013",
month = jan,
day = "1",
doi = "10.46298/dmtcs.2316",
language = "English",
series = "Discrete Mathematics & Theoretical Computer Science Proceedings",
publisher = "Maison de l'informatique et des mathematiques discretes",
pages = "469--480",
booktitle = "25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)",
address = "France",
note = "25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 ; Conference date: 24-06-2013 Through 28-06-2013",
}