G-parking functions and tree inversions
Combinatorics
2014-12-30 v2
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.
Cite
@article{arxiv.1309.2201,
title = {G-parking functions and tree inversions},
author = {David Perkinson and Qiaoyu Yang and Kuai Yu},
journal= {arXiv preprint arXiv:1309.2201},
year = {2014}
}
Comments
10 pages, 3 figures; to appear in Combinatorica