Proof of Almkvist's conjecture on the unimodality of partition polynomials

Jianxi Mao, Wenle Shi, Bao-xuan Zhu

For integers $r\ge 2$ and $n\ge 1$, let $$F_{r,n}(q)=\prod _{k=1}^n\frac{1-q^{rk}}{1-q^k}.$$ The coefficient of $q^j$ in \(F_{r,n}(q)\) counts partitions of $j$ into parts at most…