Su and Wang's real-rootedness conjecture for binomial coefficient sequences

Let $n$, $k$, $a$, and $b$ be integers such that $n\geq k\geq 0$, $b>a>0$, and $k<b$. Define

$$C_j=\binom{n+ja}{k+jb},\qquad j=0,1,\ldots.$$

Su and Wang's real-rootedness conjecture. The polynomial

$$\sum_{j\geq 0} C_j x^j$$

has only real zeros.

This conjecture concerns real-rootedness and the resulting total-positivity properties of binomial-coefficient sequences along rays of Pascal's triangle. The paper states it as one of two conjectures proposed by Su and Wang; the supplied text does not establish its resolution.