Guillaume Chapuy, Christian Stump
Published 2012-11-12, updated 2014-09-15Version 3
In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is expressed uniformly in terms of natural parameters of the group. In the case of factorizations of minimal length, we recover a formula due to P. Deligne, J. Tits and D. Zagier in the real case and to D. Bessis in the complex case. For the symmetric group, our formula specializes to a formula of D. M. Jackson.
Comments: 38 pages, including 18 pages appendix. To appear in Journal of the London Mathematical Society. v3: minor changes and corrected references; v2: added extended discussion on the definition of Coxeter elements
On Enumeration of Conjugacy Classes of Coxeter Elements
Cyclic sieving of noncrossing partitions for complex reflection groups
Polyhedral models for generalized associahedra via Coxeter elements
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