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.
@article{10_37236_9051,
author = {Westin King and Catherine H. Yan},
title = {Parking functions on directed graphs and some directed trees},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/9051},
zbl = {1441.05024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9051/}
}
TY - JOUR
AU - Westin King
AU - Catherine H. Yan
TI - Parking functions on directed graphs and some directed trees
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9051/
DO - 10.37236/9051
ID - 10_37236_9051
ER -
%0 Journal Article
%A Westin King
%A Catherine H. Yan
%T Parking functions on directed graphs and some directed trees
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9051/
%R 10.37236/9051
%F 10_37236_9051
Westin King; Catherine H. Yan. Parking functions on directed graphs and some directed trees. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9051
