  We rewrite the (extended) Ooguri-Vafa partition function for colored
HOMFLY-PT polynomials for torus knots in terms of the free-fermion
(semi-infinite wedge) formalism, making it very similar to the generating
function for double Hurwitz numbers. This allows us to conjecture the
combinatorial meaning of full expansion of the correlation differentials
obtained via the topological recursion on the Brini-Eynard-Mari\~no spectral
curve for the colored HOMFLY-PT polynomials of torus knots.
  This correspondence suggests a structural combinatorial result for the
extended Ooguri-Vafa partition function. Namely, its coefficients should have a
quasi-polynomial behavior, where non-polynomial factors are given by the Jacobi
polynomials. We prove this quasi-polynomiality in a purely combinatorial way.
In addition to that, we show that the (0,1)- and (0,2)-functions on the
corresponding spectral curve are in agreement with the extension of the colored
HOMFLY-PT polynomials data.
