Pak-Stanley labeling of the $m$-Catalan hyperplane arrangement
| Autor: | Rui Duarte, António Guedes de Oliveira |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics::Combinatorics
General Mathematics 010102 general mathematics 01 natural sciences language.human_language Shi arrangement Combinatorics Pak-Stanley labeling Hyperplane Simple (abstract algebra) Bounded function 0103 physical sciences language FOS: Mathematics Mathematics - Combinatorics Catalan 010307 mathematical physics Combinatorics (math.CO) 0101 mathematics Parking functions SIMPLE algorithm Catalan arrangement Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| DOI: | 10.48550/arxiv.1903.12108 |
| Popis: | We characterize in simple terms the Pak-Stanley labels $\lambda(R)$ of the regions $R$ of the $m$-Catalan arrangement. We also propose a simple algorithm that returns $R$ from $\lambda(R)$. Finally, we characterize in close terms the labels of the relatively bounded regions. Comment: 14 pages, 5 figures |
| Databáze: | OpenAIRE |
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