Parking Functions on Directed Graphs and Some Directed Trees
Yan, Catherine H.
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.
parking functions, mapping digraphs, edge orientations, Mathematics
King, W., & Yan, C. H. (2020). Parking functions on directed graphs and some directed trees. The Electronic Journal of Combinatorics, 27(2).