G-parking functions and tree inversions

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 solves a problem posed by R. Stanley.

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Correspondence to David Perkinson.

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Perkinson, D., Yang, Q. & Yu, K. G-parking functions and tree inversions. Combinatorica 37, 269–282 (2017). https://doi.org/10.1007/s00493-015-3191-y

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Mathematics Subject Classification (2000)

  • 05A15
  • 05A19