Bijections Between Multiparking Functions, Dirichlet Configurations, and Descending R-Traversals

There are several combinatorial objects that are known to be in bijection with the spanning trees of a graph G. These objects include G-parking functions, critical configurations of G, and descending traversals of G. In this paper, we extend the bijections to generalizations of all three objects. Partially supported by NSF VIGRE grant # 9977354.