  Andrews recently introduced k-marked Durfee symbols, which are a
generalization of partitions that are connected to moments of Dyson's rank
statistic. He used these connections to find identities relating their
generating functions as well as to prove Ramanujan-type congruences for these
objects and find relations between.
  In this paper we show that the hypergeometric generating functions for these
objects are natural examples of quasimock theta functions, which are defined as
the holomorphic parts of weak Maass forms and their derivatives. In particular,
these generating functions may be viewed as analogs of Ramanujan's mock theta
functions with arbitrarily high weight. We use the automorphic properties to
prove the existence of infinitely many congruences for the Durfee symbols.
Furthermore, we show that as k varies, the modularity of the k-marked Durfee
symbols is precisely dictated by the case k=2. Finally, we use this relation in
order to prove the existence of general congruences for rank moments in terms
of level one modular forms of bounded weight.
