%0 Journal Article
%T An overpartition analogue of the $q$-binomial coefficients
%A Jehanne Dousse
%A Byungchan Kim
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1410.5301v2