Arithmetic-progression conjecture for rank-generating functions

Let $F_{\lambda}(q)$ be the rank-generating function for partitions contained inside a partition $\lambda$, and let

$$\lambda=\langle a,a-t,\dots,a-(b-1)t\rangle$$

be a partition whose parts form an arithmetic progression. A polynomial is unimodal if its coefficients weakly increase and then weakly decrease. Arithmetic-progression unimodality conjecture. If $t\ge a/b$, then $F_{\lambda}(q)$ is unimodal. Equivalently, this asserts unimodality for all such arithmetic-progression partitions that begin with the smallest possible positive integer. The staircase case is known, but the conjecture remains open in general; the source also notes that some truncated staircases outside this range are nonunimodal.