Recently, right-angled Artin groups have attracted much attention in geometric group theory.
They have a rich structure of subgroups and nice algorithmic properties, and they give rise to …

Gamma-positivity is an elementary property that polynomials with symmetric coefficients may
have, which directly implies their unimodality. The idea behind it stems from work of Foata …

The first interesting array of numbers a typical mathematics student encounters is Pascal's
triangle, shown in Table 1.1. It has many beautiful properties, some of which we will review …

The purpose of this book is to describe the global properties of complete simply connected
spaces that are non-positively curved in the sense of AD Alexandrov and to examine the …

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive
curvature, have been of interest in many fields, including geometric (and combinatorial) …

Here, the study of torus actions on topological spaces is presented as a bridge connecting
combinatorial and convex geometry with commutative and homological algebra, algebraic …

Many important sequences in combinatorics are known to be log-concave or unimodal, but
many are only conjectured to be so although several techniques using methods from …

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and
study their f-, h-and γvectors. These polytopes include permutohedra, associahedra …

Algebraic combinatorics is concerned with the interaction between combinatorics and such
other branches of mathematics as commutative algebra, algebraic geometry, algebraic …

We begin by recalling some well-known facts. The natural action of the symmetric group Sn
on Rncan be viewed as a group generated by reflections. The reflections in Sn are the …