Torus link homology and the nabla operator

In recent work, Elias and Hogancamp develop a recurrence for the Poincaré series of the triply graded Khovanov-Rozansky homology of certain links, one of which is the (n,n) torus link. In this case, Elias and Hogancamp give a combinatorial formula for this homology that is reminiscent of the combinatorics of the modified Macdonald polynomial eigenoperator ∇. We give a combinatorial formula for the homologies of all complexes considered by Elias and Hogancamp. Our first formula is not easily computable, so we show how to transform it into a computable version. Finally, we conjecture a direct relationship between the (n,n) torus link case of our formula and the symmetric function ∇p1n.