Polynomiality of factorizations in reflection groups

We study the number of ways of factoring elements in the complex reflection groups G(r, s, n) as products of reflections. We prove a result that compares factorization numbers in G(r, s, n) to those in the symmetric group S-n, and we use this comparison, along with the Ekedahl, Lando, Shapiro, and Vainshtein (ELSV) formula, to deduce a polynomial structure for factorizations in G(r, s, n).