  The $q$-binomial coefficients
$\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$,
are known to be polynomials with non-negative integer coefficients. This
readily follows from the $q$-binomial theorem, or the many combinatorial
interpretations of $\qbinom{n}{m}$. 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.
