  The generating function of double Hurwitz numbers is known to become a tau
function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators
turn out to satisfy a set of generalized string equations. These generalized
string equations resemble those of $c = 1$ string theory except that the
Orlov-Schulman operators are contained therein in an exponentiated form. These
equations are derived from a set of intertwining relations for fermiom
bilinears in a two-dimensional free fermion system. The intertwiner is
constructed from a fermionic counterpart of the cut-and-join operator. A
classical limit of these generalized string equations is also obtained. The so
called Lambert curve emerges in a specialization of its solution. This seems to
be another way to derive the spectral curve of the random matrix approach to
Hurwitz numbers.
