Let $M$ be a matroid of rank $r$, and write
\begin{align*}
\chi_M(q) = \sum_{k=0}^{r} (-1)^k w_k(M) q^{r-k}.
\end{align*}
Then the sequence $(w_0(M), w_1(M), \dots, w_r(M))$ is log-concave:
\begin{align*}
w_k(M)^2 \ge w_{k-1}(M)w_{k+1}(M)
\end{align*}
for $1 \le k \le r-1$.