  We prove analytic and combinatorial identities reminiscent of Schur's
classical partition theorem. Specifically, we show that certain families of
overpartitions whose parts satisfy gap conditions are equinumerous with
partitions whose parts satisfy congruence conditions. Furthermore, if small
parts are excluded, the resulting overpartitions are generated by the product
of a modular form and Gordon and McIntosh's universal mock theta function.
Finally, we give an interpretation for the universal mock theta function at
real arguments in terms of certain conditional probabilities.

Number Theory