Almkvist's conjecture on the unimodality of Gaussian polynomials

Let $n$ and $r$ be positive integers, and define

$$f_{n,r}(q)=\prod_{i=1}^n\frac{1-q^{ri}}{1-q^i}.$$

Almkvist's conjecture. The polynomial $f_{n,r}(q)$ is an ${\rm A}$-polynomial if either $r$ is even and $n\ge 1$, or $r$ is odd and $n\ge 11$. This conjecture gives sufficient conditions for the Gaussian polynomial to have the coefficient properties encoded by an ${\rm A}$-polynomial. The surrounding discussion attributes it to Almkvist; the supplied text gives no evidence that it has been resolved.