  We derive an algorithm to produce explicit formulas for certain generating
functions of double Hurwitz numbers. These formulas generalize a formula of
Goulden, Jackson and Vakil for one part double Hurwitz numbers. Immediate
consequences include a new proof that double Hurwitz numbers are piecewise
polynomial, an understanding of the chamber structure and wall crossing for
these polynomials, and a proof of the Goulden, Jackson and Vakil's Strong
Piecewise Polynomiality conjecture. The method is a straightforward application
of Okounkov's expression for double Hurwitz numbers in terms of operators on
the infinite wedge. We begin with a introduction to the infinite wedge tailored
to our use.
