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.
|Original language||English (US)|
|Journal||Electronic Journal of Combinatorics|
|State||Published - Feb 16 2018|
Bibliographical noteFunding Information:
∗Supported by NSF grant DMS-1601961. †Supported by NSF grant DMS-1148634. ‡Supported by NSF grant DMS-1601961.
Supported by NSF grant DMS-1601961. † Supported by NSF grant DMS-1148634. ‡ Supported by NSF grant DMS-1601961. Work of the second author was carried out under the auspices of the 2017 summer REU program at the School of Mathematics, University of Minnesota, Twin Cities. The authors thank Craig Corsi, Theo Douvropoulos, and Joel Lewis for helpful comments, and they thank Jean Michel for allowing them to include his proof of Corollary 2.
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- Coxeter element
- Reflection group