  We claim that HOMFLY polynomials for virtual knots, defined with the help of
the matrix-model recursion relations, contain more parameters, than just the
usual $q$ and $A = q^N$. These parameters preserve topological invariance and
do not show up in the case of ordinary (non-virtual) knots and links. They are
most conveniently observed in the hypercube formalism: then they substitute
$q$-dimensions of certain fat graphs, which are not constrained by recursion
and can be chosen arbitrarily. The number of these new topological invariants
seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15,
91, 784, 9160, ... This number can be decreased by imposing the factorization
requirement for composites, in addition to topological invariance -- still
freedom remains. None of these new parameters, however, appear in HOMFLY for
Kishino unknot, which thus remains unseparated from the ordinary unknots even
by this enriched set of knot invariants.
