  We present relations between Hirota-type bilinear operators, scalar products
on spaces of symmetric functions and integrals defining matrix model partition
functions. Using the fermionic Fock space representation, a proof of the
expansion of an associated class of KP and 2-Toda tau functions $\tau_{r,n}$ in
a series of Schur functions generalizing the hypergeometric series is given and
related to the scalar product formulae. It is shown how special cases of such
$\tau$-functions may be identified as formal series expansions of partition
functions. A closed form exapnsion of $\log \tau_{r,n}$ in terms of Schur
functions is derived.
