Computation in Coxeter Groups-I. Multiplication
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Summary
An efficient and purely combinatorial algorithm for calculating products in arbitrary Coxeter groups is presented, which seems to be good enough in many interesting cases to build the minimal root reflection table of Brink and Howlett, which can be used for a more efficient multiplication routine.
- Type
- article
- Published
- 2002-06-11
- Cited by
- 13
- References
- 12
- Access
- Open access
- OpenAlex
- https://openalex.org/W92501153
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:14944516
Keywords
Coxeter group, Mathematics, Coxeter element, Artin group, Coxeter complex
References
- A finiteness property an an automatic structure for Coxeter groups
- DISCRETE LINEAR GROUPS GENERATED BY REFLECTIONS
- On the Translation of Languages from Left to Right
- Efficient string matching
- A Transducer Approach to Coxeter Groups
- GROUPES ET ALGÉBRES DE LIE
- Reflection Groups and Coxeter Groups
- Le problème des mots dans les groupes de Coxeter
Cited by
- Computing Kazhdan-Lusztig Polynomials for Arbitrary Coxeter Groups
- Solving the enumeration and word problems on Coxeter groups
- NONORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS
- Root Systems for Asymmetric Geometric Representations of Coxeter Groups
- Computation in Coxeter groups II. Constructing minimal roots
- Automata, reduced words, and Garside shadows in Coxeter groups
- ON PAIRED ROOT SYSTEMS OF COXETER GROUPS
- Growth Rates of Coxeter Groups and Perron Numbers
- HYPERTILING — a high performance Python library for the generation and visualization of hyperbolic lattices
- Codebase release 1.3 for HYPERTILING
- Hyperbolic tiling neighborhoods in O(1) time
- NON-ORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS
- ALGORITHMS, DEHN FUNCTIONS, AND AUTOMATIC GROUPS
- Integral Homology and Poincar\'e Polynomials of classical and exceptional Real Flag Manifolds
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