Between Shi and Ish
| Autor: | Rui Duarte, António Guedes de Oliveira |
|---|---|
| Přispěvatelé: | Faculdade de Ciências |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Connected component
Discrete mathematics Subfamily Conjecture Mathematics::Combinatorics Hyperplane arrangements 010102 general mathematics Dimension (graph theory) 0102 computer and information sciences 01 natural sciences Theoretical Computer Science Shi arrangement Combinatorics Pak-Stanley labeling Hyperplane Ish arrangement 010201 computation theory & mathematics Discrete Mathematics and Combinatorics 0101 mathematics Parking functions Complement (set theory) Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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