A q-rious positivity

The q-binomial coefficients [(n)(m)] = Pi(m)(i=1) (1-q(n-m+i))/(1-q(i)), for integers 0 <= m <= n, are known to be polynomials with non-negative integer coefficients. This readily follows from the q-binomial theorem, or the many combinatorial interpretations of [(n)(m)]. In this note we conjecture an arithmetically motivated generalisation of the non-negativity property for products of ratios of q-factorials that happen to be polynomials.