Sagan et al.'s unimodality conjecture for 321-avoiding permutations

For a positive integer $n$, let $S_n(321)$ be the set of 321-avoiding permutations of length $n$, and for a permutation $\sigma$, let $\operatorname{maj}(\sigma)$ and $\operatorname{des}(\sigma)$ denote its major index and number of descents. Define polynomials $A_{n,k}(q)$ by

$$\sum_{\sigma \in S_n(321)} q^{\operatorname{maj}(\sigma)}t^{\operatorname{des}(\sigma)}=\sum_{k=0}^{n-1}t^kA_{n,k}(q).$$

Sagan et al.'s conjecture. The polynomials $A_{n,k}(q)$ are unimodal.

The conjecture concerns the refined major-index distribution on 321-avoiding permutations. The paper states that it proves this conjecture, although the supplied status metadata does not specify a resolution status.