Orientations, semiorders, arrangements, and parking functions
Combinatorics
2020-08-12 v3
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
Cite
@article{arxiv.1112.5421,
title = {Orientations, semiorders, arrangements, and parking functions},
author = {Sam Hopkins and David Perkinson},
journal= {arXiv preprint arXiv:1112.5421},
year = {2020}
}
Comments
31 pages, 12 figures. v2: corrected typos. v3: substantially improved exposition; corrected typos