A combinatorial Hopf algebra is a graded connected Hopf algebra over a field is the product
(in the categorical sense) of its even and odd Hopf subalgebras. We also calculate the odd …

These notes--originating from a one-semester class by their second author at the University
of Minnesota--survey some of the most important Hopf algebras appearing in combinatorics …

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the
Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be …

We give a unified explanation of the geometric and algebraic properties of two well-known
maps, one from permutations to triangulations, and another from permutations to subsets …

We introduce bidendriform bialgebras, which are bialgebras such that both product and
coproduct can be split into two parts satisfying good compatibilities. For example, the …

A bstract We show that the counting of observables and correlators for a 3-index tensor
model are organized by the structure of a family of permutation centralizer algebras. These …

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on
the subject of symmetric groups and representation theory. Utilizing new research and …

An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate
students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is …

Abstract We survey Jean-Louis Loday's vertex description of the associahedron, and its far
reaching influence in combinatorics, discrete geometry, and algebra. We present in …

The history of quasisymmetric functions begins in 1972 with the thesis of Richard Stanley,
followed by the formal definition of the Hopf algebra of quasisymmetric functions in 1984 by …