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Title: Hyperplane arrangements between Shi and Ish
Author: Duarte, Rui
Guedes de Oliveira, António
Keywords: Hyperplane arrangements
Shi arrangement
Ish arrangement
Pak-Stanley labelling
Parking functions
Issue Date: Jul-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 this family 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 labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.
Peer review: yes
DOI: 10.1016/j.endm.2018.06.046
ISSN: 1571-0653
Publisher Version:
Appears in Collections:CIDMA - Artigos
AGG - Artigos
DMat - Artigos

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