Pak-Stanley labeling of the $m$-Catalan hyperplane arrangement

Abstract

We characterize in simple terms the Pak-Stanley labels $\lambda (R)$ of the regions $R$ of the $m$-Catalan arrangement. We also propose a simple algorithm that returns $R$ from $\lambda (R)$. Finally, we characterize in close terms the labels of the relatively bounded regions.

14 pages, 5 figures