Geodesic
The eigenvalues of hyperoctahedral descent operators and applications to card-shuffling
C. Y. Amy Pang1
1Hong Kong Baptist University
The electronic journal of combinatorics, Tome 29 (2022) no. 1
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We extend an algebra of Mantaci and Reutenauer, acting on the free associative algebra, to a vector space of operators acting on all graded connected Hopf algebras. These operators are convolution products of certain involutions, which we view as hyperoctahedral variants of Patras's descent operators. We obtain the eigenvalues and multiplicities of all our new operators, as well as a basis of eigenvectors for a subclass akin to Adams operations. We outline how to apply this eigendata to study Markov chains, and examine in detail the case of card-shuffles with flips or rotations.
DOI : 10.37236/10678
Classification : 16T30, 05E10
Mots-clés : graded connected Hopf algebras, Patras's descent operators, Adams operations

C. Y. Amy Pang  1

1 Hong Kong Baptist University 
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C. Y. Amy Pang. The eigenvalues of hyperoctahedral descent operators and applications to card-shuffling. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10678

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