, Volume 37, Issue 2, pp 269–282 | Cite as

G-parking functions and tree inversions

  • David Perkinson
  • Qiaoyu Yang
  • Kuai Yu
Original Paper


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 solves a problem posed by R. Stanley.

Mathematics Subject Classification (2000)

05A15 05A19 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Reed CollegePortlandUSA

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