Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/21736
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 |
URI: | http://hdl.handle.net/10773/21736 |
DOI: | 10.1016/j.disc.2017.09.006 |
ISSN: | 0012-365X |
Appears in Collections: | CIDMA - Artigos AGG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S0012365X17303084-main.pdf | article | 509.46 kB | Adobe PDF |
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