CIDMA, Universidade de Aveiro
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.
This is joint work with António Guedes de Oliveira.