A refined count of coxeter element reflection factorizations

Elise Delmas; Thomas Hameister; Victor Reiner

doi:10.37236/7362

A refined count of coxeter element reflection factorizations

Elise Delmas, Thomas Hameister, Victor Reiner

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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
Volume	25
Issue number	1
DOIs	https://doi.org/10.37236/7362
State	Published - 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.

Keywords

Coxeter element
Factorization
Reflection group
Well-generated

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abstract = "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.",

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AU - Delmas, Elise

AU - Hameister, Thomas

AU - Reiner, Victor

N1 - Funding Information: ∗Supported by NSF grant DMS-1601961. †Supported by NSF grant DMS-1148634. ‡Supported by NSF grant DMS-1601961.

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N2 - 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.

AB - 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.

KW - Coxeter element

KW - Factorization

KW - Reflection group

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