Bigraphical Arrangements
Combinatorics
2019-12-24 v2
Abstract
We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.
Keywords
Cite
@article{arxiv.1212.4398,
title = {Bigraphical Arrangements},
author = {Sam Hopkins and David Perkinson},
journal= {arXiv preprint arXiv:1212.4398},
year = {2019}
}
Comments
Added Remark 19 addressing arbitrary G-parking functions; minor revisions