  Let $\mathcal I_n$ and $\mathcal J_n$ denote the set of involutions and
fixed-point free involutions of $\{1, \dots, n\}$, respectively, and let
$\text{des}(\pi)$ denote the number of descents of the permutation $\pi$. We
prove a conjecture of Guo and Zeng which states that $I_n(t) := \sum_{\pi \in
\mathcal I_n} t^{\text{des}(\pi)}$ is $\gamma$-positive for $n \ge 1$ and
$J_{2n}(t) := \sum_{\pi \in \mathcal J_{2n}} t^{\text{des}(\pi)}$ is
$\gamma$-positive for $n \ge 9$. We also prove that the number of $(3412,
3421)$-avoiding permutations with $m$ double descents and $k$ descents is equal
to the number of separable permutations with $m$ double descents and $k$
descents.
