Haglund–Remmel–Wilson generalized Delta conjecture

Let $m,n,k$ be in the range for which the partially labelled Dyck-path set $\mathsf{PLD}(m,n)^{\ast k}$ is defined. Let $\Delta_{h_m}$ and $\Delta'_{e_{n-k-1}}$ be Delta operators, and let $\mathsf{dinv}(D)$, $\mathsf{area}(D)$ and $x^D$ denote the statistics and label monomial of a partially labelled Dyck path $D$. Haglund–Remmel–Wilson's generalized Delta conjecture.

$$\Delta_{h_m}\Delta'_{e_{n-k-1}}e_n=\sum_{D\in\mathsf{PLD}(m,n)^{\ast k}}q^{\mathsf{dinv}(D)}t^{\mathsf{area}(D)}x^D.$$

For $m=0$, this specializes to the Delta conjecture. The source records proofs for some cases with $m\geq1$, but the full conjecture remains open.