Parking Functions on Directed Graphs and Some Directed Trees
Combinatorics
2019-05-30 v1
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 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.
Keywords
Cite
@article{arxiv.1905.12010,
title = {Parking Functions on Directed Graphs and Some Directed Trees},
author = {Westin King and Catherine Yan},
journal= {arXiv preprint arXiv:1905.12010},
year = {2019}
}