Ma–Ma–Yeh conjecture on partial gamma-positivity of generalized Stirling permutation polynomials

Let $n\geq 1$ and $0\leq i\leq n$. Write

$$\Jsp_{n,i}(x,y,z):=\sum_{\pi\in\mathcal{JSP}_{n,i}}x^{\operatorname{asc}(\pi)}y^{\operatorname{des}(\pi)}z^{\operatorname{plat}(\pi)}$$

for the trivariate extension of $A_{n,i}(y)$. A trivariate polynomial $p(x,y,z)=\sum_i s_i(x,y)z^i$ is partial $\gamma$-positive when every coefficient $s_i(x,y)$ is homogeneous $\gamma$-positive, meaning that it is homogeneous and can be written as

$$s_i(x,y)=\sum_k\gamma_k(xy)^k(x+y)^{d-2k}$$

with all $\gamma_k\geq 0$. Ma–Ma–Yeh conjecture. For every $n\geq 1$ and $0\leq i\leq n$, the polynomial $\Jsp_{n,i}(x,y,z)$ is partial $\gamma$-positive. The conjecture concerns the coefficientwise gamma-positivity of the ascent–descent–plateau enumerators for generalized Stirling permutations; its status is not resolved in the supplied source context.