  Suppose $M$ and $N$ are positive integers and let $k = \gcd(M, N)$, $m =
M/k$, and $n=N/k$. We define a symmetric function $L_{M,N}$ as a weighted sum
over certain tuples of lattice paths. We show that $L_{M,N}$ satisfies a
generalization of Mellit and Hogancamp's recursion for the triply-graded
Khovanov--Rozansky homology of the $M,N$-torus link. As a corollary, we obtain
the triply-graded Khovanov--Rozansky homology of the $M,N$-torus link as a
specialization of $L_{M,N}$. We conjecture that $L_{M,N}$ is equal (up to a
constant) to the elliptic Hall algebra operator $\mathbf{Q}_{m,n}$ composed $k$
times and applied to 1.
