A Refined Count of Coxeter Element Reflection Factorizations
Copyright policy )A Refined Count of Coxeter Element Reflection Factorizations
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.
- University of Minnesota System United States
- University of Wisconsin–Madison United States
- University of Minnesota United States
- University of Wisconsin–Oshkosh United States
- University of Minnesota Morris United States
Reflection and Coxeter groups (group-theoretic aspects), factorization, Exact enumeration problems, generating functions, well-generated group, reflection group, Coxeter element, Combinatorial aspects of groups and algebras
Reflection and Coxeter groups (group-theoretic aspects), factorization, Exact enumeration problems, generating functions, well-generated group, reflection group, Coxeter element, Combinatorial aspects of groups and algebras
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