# Pak-Stanley labeling of hyperplane arrangements

### online | 2021-11-09 | 14:30

Rui Duarte

In the nineties Pak and Stanley introduced a construction in which every region of the $m$-Shi arrangement of hyperplanes is labeled with an $m$-parking function. In this talk we consider the same construction applied to the regions of the $m$-Catalan arrangement and of the Ish arrangement. We characterize the Pak-Stanley labels of the regions of both arrangements and present an algorithm for the inverse. Finally, we characterize the labels of the relatively bounded regions of both arrangements.