A refined count of coxeter element reflection factorizations

Elise Delmas, Thomas Hameister, Victor Reiner

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - Feb 16 2018

Bibliographical note

Funding Information:
∗Supported by NSF grant DMS-1601961. †Supported by NSF grant DMS-1148634. ‡Supported by NSF grant DMS-1601961.


  • Coxeter element
  • Factorization
  • Reflection group
  • Well-generated

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