Combinatorial interpretation of the q-analogue

Identify a natural combinatorial interpretation for the q-analogue r_q(n) defined by replacing the rising-factorial factors in the partition formula for r(n) with Gaussian binomial coefficients.

Background

The paper defines r_q(n) as a partition sum involving Gaussian binomial coefficients and proves that its generating function has a q-Pochhammer product representation. Although this construction is an algebraic q-analogue of the original coefficient formula, the authors leave unresolved whether it counts a natural class of combinatorial objects.