Haglund–Haiman–Loehr–Remmel–Ulyanov Shuffle Conjecture

Let $\mathsf{DR}_n$ be the doubly graded diagonal coinvariant ring, and let $\mathsf{PF}_n$ be the labeled classical parking functions. For each $P$, let $\mathsf{area}(P)$, $\mathsf{dinv}(P)$, $\mathsf{area'}(\mathsf{\zeta}(P))$, and $\mathsf{IDes}(P)$ have the meanings defined in the source, and let $F_{n,S}(\mathbf{x})$ be Gessel's fundamental quasisymmetric function. Shuffle Conjecture.

$$\mathsf{Frob}_{\mathsf{DR}_n}(\mathbf{x};q,t)=\sum_{P\in\mathsf{PF}_n}q^{\mathsf{area}(P)}t^{\mathsf{area'}(\mathsf{\zeta}(P))}F_{n,\mathsf{IDes}(P)}(\mathbf{x})=\sum_{P\in\mathsf{PF}_n}q^{\mathsf{area}(P)}t^{\mathsf{dinv}(P)}F_{n,\mathsf{IDes}(P)}(\mathbf{x}).$$

This refines the Hilbert-series conjecture to the bi-graded Frobenius characteristic and is historically called the Shuffle Conjecture; the supplied text does not state its resolution.