Orientations, Semiorders, Arrangements, and Parking Functions

  • Sam Hopkins
  • David Perkinson
Keywords: hyperplane arrangements, semiorders, parking functions, abelian sandpile model

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.

Published
2012-10-25
Article Number
P8