This research monograph is divided into three parts. Broadly speaking, Part I belongs to the
realm of category theory, while Parts II and III pertain to algebraic combinatorics, although …

This book gives an introduction to and an overview of the methods used in the combinatorics
of pattern avoidance and pattern enumeration in set partitions, a very active area of research …

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 …

We introduce a general and systematic theoretical framework for operational dynamic
modeling (ODM) by combining a kinematic description of a model with the evolution of the …

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 …

We uncover the structure of the space of symmetric functions in non-commutative variables
by showing that the underlined Hopf algebra is both free and co-free. We also introduce the …

In 1896, after correspondence with Dedekind, Frobenius published two papers in which
group character theory was introduced and was used to describe the factorization of the …

We discover new linear relations between the chromatic symmetric functions of certain
sequences of graphs and apply these relations to find new families of $ e $-positive unit …

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric
functions. The bases for this algebra are indexed by set partitions. We show that there exists …

We propose several constructions of commutative or cocommutative Hopf algebras based
on various combinatorial structures and investigate the relations between them. A …