Parking functions and Łukasiewicz paths

We present a bijection between two well-known objects in the ubiquitous Catalan family: non-decreasing parking functions and ukasiewicz paths.This bijection maps the maximum displacement of a parking function to the height of the corresponding ukasiewicz path, and the total displacement to the area of the path.We also study this bijection restricted to two specific families of parking functions: unit-interval parking functions and prime parking functions.