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 …

We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired
by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We give …

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 …

Let T be an unrooted tree. The chromatic symmetric functionXT, introduced by Stanley, is a
sum of monomial symmetric functions corresponding to proper colorings of T. The subtree …

In 1995 Stanley introduced the chromatic symmetric function XG associated to a simple
graph G as a generalization of the chromatic polynomial of G. In this paper we present a …

We extend the definition of the chromatic symmetric function XG to include graphs G with a
vertex-weight function w: V (G)→ N. We show how this provides the chromatic symmetric …

We use P-tableaux to give a combinatorial proof of the e-positivity of chromatic quasi-
symmetric functions with bounce number two and some of those with bounce number three …

We compute an explicit e-positive formula for the chromatic symmetric function of a lollipop
graph, L_m,n. From here we deduce that there exist countably infinite distinct e-positive and …

In this article we show how to compute the chromatic quasisymmetric function of indifference
graphs from the modular law introduced in [19]. We provide an algorithm which works for …

Consider the algebra $\mathbb {Q}\langle\langle x_1, x_2,\ldots\rangle\rangle $ of formal
power series in countably many noncommuting variables over the rationals. The subalgebra …