  We apply a new statistics, the factorial moment correlators, to density maps
obtained from the APM survey. The resulting correlators are all proportional to
the two point correlation function, substantially amplified, with an
amplification nearly exponential with the total rank of the correlators. This
confirms the validity of the hierarchical clustering assumption on the dynamic
range examined, corresponding to $0.5 \hmpc - 50 \hmpc$ in three dimensional
space. The Kirkwood superposition with loop terms is strongly rejected. The
structure coefficients of the hierarchy are also fitted. The high quality of
the APM catalog enabled us to disentangle the various contributions from the
power spectrum, small scale nonlinear clustering, and combinatorial effects,
all of which affect the amplification of the correlators. These effects should
appear in correlations of clusters in a similar fashion.
