105 citations · 114 across the 9 of their papers we have counts for
9 papers
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Marcelo Aguiar, Carlos Andre, Carolina Benedetti +25
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a fi…
Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras
Samuel K. Hsiao, Gizem Karaali
We develop a theory of multigraded (i.e., -graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and S…
A semigroup approach to wreath-product extensions of Solomon's descent algebras
Samuel K. Hsiao
There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semig…
Random walks on quasisymmetric functions
Patricia Hersh, Samuel K. Hsiao
Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random wal…
Peak Quasisymmetric Functions and Eulerian Enumeration
Louis J. Billera, Samuel K. Hsiao, Stephanie van Willigenburg
Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly…
Colored posets and colored quasisymmetric functions
Samuel K. Hsiao, T. Kyle Petersen
The colored quasisymmetric functions, like the classic quasisymmetric functions, are known to form a Hopf algebra with a natural peak subalgebra. We show how these algebras arise a…