Bigraphical arrangements
2014 ◽
Vol DMTCS Proceedings vol. AT,...
(Proceedings)
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Keyword(s):
International audience 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 $\textit{Transactions of the American Mathematical Society}$
Keyword(s):
1906 ◽
Vol 12
(5)
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pp. 223-235
2006 ◽
Vol 38
(04)
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pp. 696-697