Hurwitz numbers for reflection groups III: Uniform formulas
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales
TL;DR
This paper provides uniform formulas for counting full reflection factorizations of certain elements in Weyl and complex reflection groups, extending previous results on Hurwitz numbers.
Contribution
It introduces generalized, uniform formulas for reflection factorizations in Weyl and complex reflection groups, building on prior work on Hurwitz numbers.
Findings
Derived explicit formulas for reflection factorizations
Unified approach applicable to various reflection groups
Extended genus-0 Hurwitz number formulas to broader contexts
Abstract
We give uniform formulas for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus-0 Hurwitz numbers. This paper is the culmination of a series of three.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality