The e-positivity conjecture for chromatic quasisymmetric functions of indifference graphs

Let $\gamma$ be an indifference graph, and write its chromatic quasisymmetric function in the elementary symmetric-function basis as

$$X_{\gamma}(\mathbf{x};t)=\sum_{\lambda}a_{\lambda}(t)e_{\lambda}.$$

The e-positivity conjecture. For each $\gamma \in \mathcal{I}\mathcal{G}$, $X_{\gamma}(\mathbf{x};t)$ is $e$-positive; equivalently, $a_{\lambda}(t)\in\mathbb{Z}_{\geq 0}[t]$ for every partition $\lambda$.

This conjecture generalizes the Stanley–Stembridge conjecture, whose $t=1$ case is known. The full polynomial positivity statement remains open.