On Parity Unimodality of $q$-Catalan Polynomials

Guoce Xin, Yueming Zhong

A polynomial $A(q)={\sum }_{i=0}^n{a}_i{q}^i$ is said to be unimodal if $a_0\le a_1\le \cdots \le a_k\ge a_{k+1}\ge \cdots \ge a_n$. We investigate the unimodality of rational $q$-Catal…