Nadeau–Tewari sign conjecture for staircase-basis coefficients

Let $\lambda$ be a partition inside an $n\times m$ board with $n\leq m$, and let $\delta_j=(j,j-1,\ldots,1)$ be the staircase partition. Write the chromatic quasisymmetric function in the staircase basis as

$$X_\lambda({\bf x},q)=\sum_{j=0}^{n}a_j^{m,n}(\lambda,q)X_{\delta_j}({\bf x},q).$$

Nadeau–Tewari sign conjecture. For fixed $j$, $a_j^{m,n}(\lambda,q)$ is a Laurent polynomial in $q$ whose coefficients are integers of the same sign.

These coefficients describe the transition from chromatic quasisymmetric functions indexed by Ferrers boards to the staircase basis. The source records that this conjecture was proved by Nadeau–Tewari.