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Séminaire Lotharingien de Combinatoire, 78B.38 (2017), 11 pp.

# Andrew Timothy Wilson

# Torus Link Homology and the Nabla Operator

**Abstract.**
In recent work, Elias and Hogancamp develop a recurrence for the
Poincar\'e series of the triply graded Hochschild 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 links 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 ∇*p*_{1n}.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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