  We consider series over Young diagrams of products of Schur functions
$s_{\lambda\cup\lambda}$, marked with ``fat partitions'' $\lambda\cup\lambda$,
which appear in matrix models associated with ensembles of symplectic and
orthogonal matrices and quaternion ensemble Ginibre. We consider mixed matrix
models that also contain complex Ginibre ensembles labeled by graphs and the
three ensembles mentioned above. Cases are identified when the series of
perturbations in coupling constants turn out to be tau functions of the DKP
hierarchy introduced by the Kyoto school. This topic relates matrix models to
random partitions - discrete symplectic ensemble and its modifications.
