English

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

R2 v1 2026-06-21T19:56:02.552Z