Eigenvalues of symmetrized shuffling operators

Abstract

This paper describes a combinatorial way of obtaining all the eigenvalues of the symmetrized shuffling operators introduced by Victor Reiner, Franco Saliola and Volkmar Welker. It allows us to prove their conjecture that these eigenvalues are integers. This work generalizes the case of the random-to-random Markov chain.

arXiv comment12 pages. Extended abstract accepted for FPSAC 2019. It will appear in Séminaire Lotharingien de combinatoire

Cited by in corpus (1)

• Random Walks on the Symmetric Group: Cutoff for One-sided Transposition Shuffles