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arXiv · 1905.12010

Parking Functions on Directed Graphs and Some Directed Trees

Westin King·Catherine Yan
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Abstract

Classical parking functions can be defined in terms of drivers with preferred parking spaces searching a linear parking lot for an open parking spot. We may consider this linear parking lot as a collection of $n$ vertices (parking spots) arranged in a directed path. We generalize this notion to allow for more complicated "parking lots" and define parking functions on arbitrary directed graphs. We then consider a relationship proved by Lackner and Panholzer between parking functions on trees and "mapping digraphs" and we show that a similar relationship holds when edge orientations are reversed.

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Westin King, Catherine Yan. 2019-05-28. Parking Functions on Directed Graphs and Some Directed Trees. https://arxiv.org/abs/1905.12010

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