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Author(s): Duarte, R
António Guedes de Oliveira
Title: Between Shi and Ish
Issue Date: 2018
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.
Document Type: Artigo em Revista Científica Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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