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 maximal 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.
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Selig et al. (2024) studied this question.
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