Su and Wang's log-concavity-to-log-convexity conjecture for binomial coefficient sequences

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

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

is defined by these binomial coefficients. Su and Wang's log-concavity-to-log-convexity conjecture. There exists an integer $m\geq 0$ such that this sequence is log-concave for $0\leq j\leq m$ and log-convex for $j\geq m$.

This conjecture describes a single transition between log-concavity and log-convexity along a ray of Pascal's triangle. The abstract states that the paper proves the claim using a variation-diminishing property of the Laplace transform.