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math.CO2021
Hopf algebras of parking functions and decorated planar trees
Nantel Bergeron, Rafael S. González D'León, Shu Xiao Li +2
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled…
math.CO2021
The Eigenvalues of Hyperoctahedral Descent Operators and Applications to Card-Shuffling
C. Y. Amy Pang
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…