Bringmann, KathrinKathrinBringmannLovejoy, JeremyJeremyLovejoyOsburn, RobertRobertOsburn2016-08-222016-08-222009 the A2010International Mathematics Research Noticeshttp://hdl.handle.net/10197/7822We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called quasimock theta functions, while a fourth specialization gives quasimodular forms. We then define a two-parameter generalization of Andrews' smallest parts function and note that this leads to quasimock theta functions as well. The automorphic properties are deduced using q-series identities relating the relevant generating functions to known mock theta functions.enThis article has been accepted for publication in International Mathematics Research Notices ©: 2010 the Authors. Published by Oxford University Press. All rights reserved.Partitions of integersModular functionsAutomorphic functionsJournal Article223826010.1093/imrn/rnp1312016-08-10https://creativecommons.org/licenses/by-nc-nd/3.0/ie/