  We derive explicit formulae for the generating series of mixed Grothendieck
dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge
formalism. This reveals the strong piecewise polynomiality in the sense of
Goulden-Jackson-Vakil, generalising a result of Johnson, and provides a new
explicit proof of the piecewise polynomiality of the mixed case. Moreover, we
derive wall-crossing formulae for the mixed case. These statements specialise
to any of the three types of Hurwitz numbers, and to the mixed case of any
pair.
