The notion of parking functions was introduced by Konheim and Weiss [53] as a colorful way
to describe their work on computer storage. The parking problem can be stated as follows …

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 …

We study the relationship between rational slope Dyck paths and invariant subsets in Z,
extending the work of the first two authors in the relatively prime case. We also find a …

Let Z_m^k consist of the mk alcoves contained in the m-fold dilation of the fundamental
alcove of the type A k affine hyperplane arrangement. As the fundamental alcove has a …

The shuffle conjecture (due to Haglund, Haiman, Loehr, Remmel, and Ulyanov) provides a
combinatorial formula for the Frobenius series of the diagonal harmonics module DH n …

Parking functions are multifaceted objects with applications in many areas of mathematics.
For a graph G on n+ 1 vertices with a designated vertex as root, Postnikov and Shapiro …

Abstract The Shuffle Theorem, recently proven by Carlsson and Mellit, states that the
bigraded Frobenius characteristic of the diagonal harmonics is equal to a weighted sum of …