Factorization conjecture for Kazhdan–Lusztig R-polynomials of 321-avoiding 2-repeating permutations

Let $w\in \mathfrak{S}_n$ be a $321$-avoiding and $2$-repeating permutation. Let $u,v\in\mathfrak{S}_n$ satisfy $u\leq v\leq w$, and let $\tilde{R}_{u,v}(t)$ denote the corresponding Kazhdan–Lusztig $R$-polynomial. Factorization conjecture. There exist integers $a,b$ and $c_i$ such that

$$\tilde{R}_{u,v}(t)=t^{a}\prod_{i=1}^{b}\mathcal{F}_{c_i}(t).$$

The conjecture proposes a closed product formula when the upper permutation is 321-avoiding and 2-repeating. It is motivated by diagrammatic computations in which a small number of higher-valent vertices still appears compatible with factorization, but the general interaction of letters in such diagrams remains difficult to control; the source gives no resolution of the conjecture.