Séminaire Lotharingien de Combinatoire, 82B.78 (2019), 12 pp.

Nadia Lafrenière

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.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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