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 perform a key step towards a purely combinatorial proof of topological recursion for colored HOMFLY-PT polynomials for torus knots: we prove the quasi-polynomiality property of the coefficients of the extended Ooguri-Vafa partition function in a purely combinatorial way. Non-polynomial factors are related to Jacobi polynomials, regarding which we obtain some new results on the 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 colored HOMFLY-PT polynomials data. 查看全文>>