Orientations, Semiorders, Arrangements, and Parking Functions

Sam Hopkins, David Perkinson

Abstract


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.


Keywords


hyperplane arrangements, semiorders, parking functions, abelian sandpile model

Full Text: PDF