We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

This monograph studies the interplay between various algebraic, geometric and
combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and …

The “classical” parking functions, counted by the Cayley number (n+ 1) n− 1, carry a natural
permutation representation of the symmetric group S n in which the number of orbits is the …

We introduce a new approach to the enumeration of rational slope parking functions with
respect to the $\operatorname {area} $ and a generalized $\operatorname {dinv} $ statistics …

Enumerative combinatorics is about counting. The typical question is to find the number of
objects with a given set of properties. However, enumerative combinatorics is not just about …

An m-ballot path of size n is a path on the square grid consisting of north and east unit steps,
starting at (0, 0), ending at (mn, n), and never going below the line {x= my}. The set of these …

This paper is about two arrangements of hyperplanes. The first—the Shi arrangement—was
introduced by Jian-Yi Shi (1986) to describe the Kazhdan-Lusztig cells in the affine Weyl …

A special case of Haimanʼs identity [M. Haiman, Vanishing theorems and character
formulas for the Hilbert scheme of points in the plane, Invent. Math. 149 (2002) 371–407] for …

For an irreducible crystallographic root system Φ and a positive integer p relatively prime to
the Coxeter number h of Φ, we give a natural bijection A from the set W˜ p of affine Weyl …

We study two combinatorial miracles relating purely poset-theoretic objects with purely
Coxeter-theoretic objects. The first miracle is that there are the same number of linear …