G-parking functions and tree inversions

Published 9 Sep 2013 in math.CO | (1309.2201v2)

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.

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