G-parking functions and tree inversions

2013/09/09 by David Perkinson, Qiaoyu Yang, Perkinson, David +3
Computer Science · Mathematics · #05A15 #05A19 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1309.2201

openalex publication_date 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A depth-first search version of Dhar's burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the spanning tree. Specializing to the complete graph answers a problem posed by R. Stanley.

Related

• A family of bijections between G-parking functions and spanning trees
• Inversions in parking functions
• Bijections Between Multiparking Functions, Dirichlet Configurations, and Descending R-Traversals
• Bijection: Parking-like structures and Tree-like structures
• Generalized Bijective Maps between G-Parking Functions, Spanning\n Trees, and the Tutte Polynomial