Elise delMas, Thomas Hameister, Victor Reiner
Published 2017-08-21Version 1
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 number of 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.
What fraction of an $S_n$-orbit can lie on a hyperplane?
The fraction of an $S_n$-orbit on a hyperplane
Cyclic sieving of noncrossing partitions for complex reflection groups
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