  Recently we introduced the hypergraph matrix model (HMM), a Hermitian matrix
model generalizing the classical Gaussian Unitary Ensemble (GUE). In this model
the Gaussians of the GUE, whose moments count partitions of finite sets into
pairs, are replaced by formal measures whose moments count set partitions into
parts of a fixed even size 2m >= 2. Just as the expectations of the trace
polynomials Tr X^{2r} in the GUE produce polynomials counting unicellular
orientable maps of different genera, in the HHM these expectations give
polynomials counting certain unicelled edge-ramified CW complexes with extra
data that we call (orientable CW) maps with instructions. In this paper we
describe generating functions for maps with instructions of fixed genus and
with the number of vertices arbitrary. Our results are motivated by work of
Wright. In particular Wright computed generating functions of connected graphs
of fixed first Betti number as rational functions in the rooted tree function T
(x), given as the solution to the functional relation x = T e^{-T}.
