  Okounkov's generating function of the double Hurwitz numbers of the Riemann
sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense
of Orlov and Scherbin. This tau function turns into a tau function of the
lattice KP hierarchy by specializing one of the two sets of time variables to
constants. When these constants are particular values, the specialized tau
functions become solutions of various reductions of the lattice KP hierarchy,
such as the lattice Gelfand-Dickey hierarchy, the Bogoyavlensky-Itoh-Narita
lattice and the Ablowitz-Ladik hierarchy. These reductions contain previously
unknown integrable hierarchies as well.
