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Discrete Mathematics & Theoretical Computer Science |
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. The full version of this paper is forthcoming in the $\textit{Transactions of the American Mathematical Society}$
Source : ScholeXplorer
IsRelatedTo ARXIV 0801.1114 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.disc.2010.01.002 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0801.1114
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