Parking distributions on trees. (October 2017) - Butler, Steve; Graham, Ron; Yan, Catherine H.
Abstract: We consider a generalization of parking functions to parking distributions on trees and study the unordered version and a q -analogue. We give an efficient way to form generating functions to compute these values and establish the positivity and log-concavity of a related polynomial. We also connect the unordered parking distributions on caterpillars (trees whose removal of leaves results in a path) to restricted lattice walks.