  We show that the numbers of generations and anti-generations of a (2,2)
string compactification with diagonal internal theory can be expressed in terms
of certain specifications of the elliptic genus of the untwisted internal
theory which can be computed from the Poincare polynomial. To establish this
result we show that there are no cancellations of positive and negative
contributions to the Euler characteristic within a fixed twisted sector. For
our considerations we recast the orbifolding procedure into an algebraic
language using simple currents. Turning the argument around, this allows us to
define the `extended Poincare polynomial' P(t,x), which encodes information on
the orbits of the spinor current under fusion, for non-diagonal N=2
superconformal field theories. As an application, we derive an explicit formula
for P(t,x) for general Landau-Ginzburg orbifolds.
