A Refined Count of Coxeter Element Reflection Factorizations
| Autor: | Thomas Hameister, Elise G. delMas, Victor Reiner |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
Generating function Theoretical Computer Science Combinatorics Reflection (mathematics) Computational Theory and Mathematics Hyperplane Simple (abstract algebra) Product (mathematics) Discrete Mathematics and Combinatorics Geometry and Topology Orbit (control theory) Reflection group Coxeter element Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 25 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/7362 |
| Popis: | For well-generated complex reflection groups, Chapuy and Stump gave a simple product for a generating function counting reflection factorizations of a Coxeter element by their length. This is refined here to record the numberof reflections used from each orbit of hyperplanes. The proof is case-by-case via the classification of well-generated groups. It implies a new expression for the Coxeter number, expressed via data coming from a hyperplane orbit; a case-free proof of this due to J. Michel is included. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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