A family of bijections between G-parking functions and spanning trees
Combinatorics
2007-05-23 v4
Abstract
For a directed graph G on vertices {0,1,...,n}, a G-parking function is an n-tuple (b_1,...,b_n) of non-negative integers such that, for every non-empty subset U of {1,...,n}, there exists a vertex j in U for which there are more than b_j edges going from j to G-U. We construct a family of bijective maps between the set P_G of G-parking functions and the set T_G of spanning trees of G rooted at 0, thus providing a combinatorial proof of |P_G| = |T_G|.
Cite
@article{arxiv.math/0307292,
title = {A family of bijections between G-parking functions and spanning trees},
author = {Denis Chebikin and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:math/0307292},
year = {2007}
}
Comments
11 pages, 4 figures; a family of bijections containing the two original bijections is presented; submitted to J. Combinatorial Theory, Series A