Abstract
We prove that the degree of the Hilbert polynomial of the HOMFLYPT homology of a closed braid [Formula: see text] is [Formula: see text], where [Formula: see text] is the number of components of [Formula: see text]. This controls the growth of the HOMFLYPT homology with respect to its polynomial grading. The Hilbert polynomial also reveals a link polynomial hidden in the HOMFLYPT polynomial.
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