Please use this identifier to cite or link to this item:
Title: Between Shi and Ish
Author: Duarte, Rui
Guedes de Oliveira, António
Keywords: Hyperplane arrangements
Shi arrangement
Ish arrangement
Pak-Stanley labeling
Parking functions
Issue Date: Feb-2018
Publisher: Elsevier
Abstract: We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family.
Peer review: yes
DOI: 10.1016/j.disc.2017.09.006
ISSN: 0012-365X
Appears in Collections:CIDMA - Artigos
AGG - Artigos

Files in This Item:
File Description SizeFormat 
1-s2.0-S0012365X17303084-main.pdfarticle509.46 kBAdobe PDF    Request a copy

FacebookTwitterDeliciousLinkedInDiggGoogle BookmarksMySpace
Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.