Geodesic
A refined count of Coxeter element reflection factorizations
Elise delMas1 ; Thomas Hameister2 ; Victor Reiner1
1Univ. of Minnesota
2Univ. of Wisconsin - Madison
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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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.
DOI : 10.37236/7362
Classification : 20F55, 05A15, 05E16
Mots-clés : reflection group, Coxeter element, factorization, well-generated group

Elise delMas  1   ; Thomas Hameister  2   ; Victor Reiner  1

1 Univ. of Minnesota
2 Univ. of Wisconsin - Madison 
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Elise delMas; Thomas Hameister; Victor Reiner. A refined count of Coxeter element reflection factorizations. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7362

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