Haglund–Remmel–Wilson's partially labelled Dyck path Delta conjecture

Let $\mathsf{PDP}(m,n)^{\star k}$ be the set of partially labelled Dyck paths of size $m+n+1$ with $n+1$ nonzero labels, $m$ zero labels attached to valleys, and $k$ decorated rises. Let $\mathsf{dinv}(P)$ and $\underline{\mathsf{area}}(P)$ be the corresponding statistics, and let $x^P$ be the product of the variables indexed by the nonzero labels of $P$. The symbols $\Delta_{h_m}$ and $\Delta'_{e_{n-k}}$ denote the Delta operators associated with $h_m$ and the primed elementary symmetric function, respectively.

Haglund–Remmel–Wilson's conjecture. For $m\geq 0$, $n\geq 0$, and $k\geq 0$,

$$\Delta_{h_m}\Delta'_{e_{n-k}}e_{n+1}=\sum_{P\in\mathsf{PDP}(m,n)^{\star k}}q^{\mathsf{dinv}(P)}t^{\underline{\mathsf{area}}(P)}x^P.$$

The source attributes this conjecture to Haglund, Remmel, and Wilson (2015) as a generalization of the Delta conjecture; no resolution is supplied in the paper.