Polynomials with palindromic and unimodal coefficients

Hua Sun, Yi Wang, Hai-Xia Zhang

Let $f(q)=a_r{q}^r+\cdots +a_s{q}^s$, with $a_r\ne 0$ and $a_s\ne 0$, be a real polynomial. It is a palindromic polynomial of darga $n$ if $r+s=n$ and $a_{r+i}=a_{s-i}$ for all $i$. P…