Between Shi and Ish

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Duarte, R (Author) Other; António Guedes de Oliveira (Author) FCUP

Journal

Title: Discrete Mathematics

Vol. 341

Pages: 388-399

ISSN: 0012-365X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00N-2PF

DOI: 10.1016/j.disc.2017.09.006

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12