  We define an overpartition analogue of Gaussian polynomials (also known as
$q$-binomial coefficients) as a generating function for the number of
overpartitions fitting inside the $M \times N$ rectangle. We call these new
polynomials over Gaussian polynomials or over $q$-binomial coefficients. We
investigate basic properties and applications of over $q$-binomial
coefficients. In particular, via the recurrences and combinatorial
interpretations of over q-binomial coefficients, we prove a Rogers-Ramaujan
type partition theorem.
