Orientations, Semiorders, Arrangements, and Parking Functions

Sam Hopkins, David Perkinson


It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph $G$, we define the $G$-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all $G$-parking functions.


hyperplane arrangements, semiorders, parking functions, abelian sandpile model

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