Abstract
The Pak-Stanley labeling is a bijection between the regions of them -Shi arrangement and them -parking functions. Mazin generalized this labeling to every deformation of the braid arrangement and proved that this labeling is always surjective onto a set of directed multigraph parking functions. We provide a right inverse to the generalized Pak-Stanley labeling, and identify a classš¯“’of arrangements for which this labeling is bijective. The classš¯“’includes the multi-Shi arrangements and the multi-Catalan arrangements. We also show that the arrangements inš¯“’are the only transitive arrangements for which the generalized Pak-Stanley labeling is bijective.