Parking distributions on trees. (October 2017)

• Record Type: Journal Article
• Authors: Butler, Steve; Graham, Ron; Yan, Catherine H.
• Is Part Of: European journal of combinatorics. Volume 65(2017)
• Page Start: 168
• Page End: 185
• Publication Date: 2017-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2017.06.003
• Languages: English
• ISSNs: 0195-6698

Abstract

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.