A q-rious positivity

The q-binomial coefficients [ⁿ_m] = ᴨ^m_i=1(1-q^n-m+i)/(1-qⁱ), 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.