On enumerating factorizations in reflection groups

We describe an approach, via Malle’s permutation Ψ on the set of irreducible characters Irr(W) of a reflection group W, that gives a uniform derivation of the Chapuy–Stump formula for the enumeration of reflection factorizations of a Coxeter element c of W. It also recovers its weighted generalization by delMas, Reiner, and Hameister, and further produces structural results for factorization formulas of arbitrary regular elements.