The braid and the Shi arrangements and the Pak-Stanley labelling

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Rui Duarte (Author) Other; Antonio Guedes de Oliveira (Author) FCUP

Journal

Title: European Journal of Combinatorics

Vol. 50

Pages: 72-86

ISSN: 0195-6698

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 2 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00G-CGV

DOI: 10.1016/j.ejc.2015.03.017

Abstract (EN): In this article we study a construction, due to Pak and Stanley, with which every region R of the Shi arrangement is (bijectively) labelled with a parking function lambda(R). In particular, we construct an algorithm that returns Rout of lambda(R). This is done by relating lambda to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that lambda(-1)(f) subset of S. We also prove that lambda maps the bounded regions of the Shi arrangement bijectively onto the prime parking functions. Finally, we introduce a variant (that we call "s-parking") of the parking algorithm that is in the very origin of the term "parking function". S-parking may be efficiently used in the context of our new algorithm, but we show that in some (well defined) cases it may even replace it.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15