  This paper gives a polynomial invariant for flat virtual links. In the case
of one component, the polynomial specializes to Turaev's virtual string
polynomial. We show that Turaev's polynomial has the property that it is
non-zero precisely when there is no filamentation of the knot, as described by
Hrencecin and Kauffman. Schellhorn has provided a version of filamentations for
flat virtual links. Our polynomial has the property that if there is a
filamentation, then the polynomial is 0. The converse fails, although if the
polynomial is 0, then it turns out to be easy to determine if there is a
filamentation.
