Orientations, Semiorders, Arrangements, and Parking Functions
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
How to Cite
Hopkins, S., & Perkinson, D. (2012). Orientations, Semiorders, Arrangements, and Parking Functions. The Electronic Journal of Combinatorics, 19(4), P8. https://doi.org/10.37236/2684
Article Number
P8