Partitio et Emergo A Note on the Computation of Eigenvalues of a Shuffle Matrix

The transition matrix of the Markov chain describing card shuffling (“shuffle matrix”) is studied. The authors propose a method to compute (a subset of) the eigenvalues of a shuffle matrix, which is a generalization of a method proposed by Doner and Uppuluri [2]. The method works by defining Markov chains with smaller state spaces than the original state space, the transition matrices of which have eigenvalues which are a subset of the eigenvalues of the shuffle matrix. corresponding author: Frans Schalekamp Cornell University Operations Research & Industrial Engineering 257 Rhodes Hall Ithaca NY 14853 [email protected] Anke van Zuylen [email protected] *This note is the result of a master’s thesis written while both authors were at the Vrije University, Amsterdam, The Netherlands, with Professor Henk Tijms as advisor.