A family of bijections between G-parking functions and spanning trees

@article{Chebikin2005AFO,
  title={A family of bijections between G-parking functions and spanning trees},
  author={Denis Chebikin and Pavlo Pylyavskyy},
  journal={J. Comb. Theory, Ser. A},
  year={2005},
  volume={110},
  pages={31-41}
}
For a directed graph G on vertices {0, bn) of non-negative integers such that, for every non-empty subset U ⊆ {1,. .. , n}, there exists a vertex j ∈ U for which there are more than bj edges going from j to G − U. We construct a family of bijective maps between the set PG of G-parking functions and the set TG of spanning trees of G rooted at 0, thus providing a combinatorial proof of |PG| = |TG|. 

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