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
. Just as the expectations
of the trace polynomials
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. 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 his computation of generating functions of
connected graphs of fixed first Betti number as rational functions in the rooted tree function
(the solution to the
functional relation
).
