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.
Highlights
Parking functions were first defined by Konheim and Weiss [8] during their study of the linear probing solution to collisions on hash tables
We gave several equivalent characterizations of an extension of the “drivers searching for a parking space” description of parking functions to digraphs
We follow the work of Lackner and Panholzer to show many of their results on trees with edges oriented towards a root still hold when the edge orientation is reversed
Summary
Parking functions were first defined by Konheim and Weiss [8] during their study of the linear probing solution to collisions on hash tables. 2) If the current vertex is unoccupied, the driver parks there If it is occupied, the driver drives to the vertex, following edge orientation, and repeats Step 2. A sequence s such that all n drivers successfully park is called a classical parking function of length n. A classical parking function of length n is a sequence s ∈ [n]n such that for all i ∈ [n],. We may consider the case when m n drivers attempt to park We call these (n, m)-parking functions and the definition is the same as in the classical case for s ∈ [n]m.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
