Andrews–Merca–Guo–Zeng conjecture on truncated Jacobi triple product coefficients

Let $k$, $R$, and $S$ be positive integers with $1\leq S<R/2$. For $n\geq1$, consider the coefficient of $q^n$ in

$$(-1)^{k-1}\frac{\sum_{j=0}^{k-1}(-1)^j q^{Rj(j+1)/2-Sj}\left(1-q^{(2j+1)S}\right)}{(q^S,q^{R-S},q^R;q^R)_\infty}.$$

Andrews–Merca–Guo–Zeng conjecture. This coefficient is nonnegative. This conjecture is solved: it was proved analytically by Mao and combinatorially by Yee in 2015, and later reproved by Wang and Yee using Bailey-pair methods.