We analyse the two--dimensional all--sky distribution of rich Abell and ACO
galaxy clusters by using counts in cells and measuring the high--order
area--averaged angular correlation functions. Confirming previous results, we
find a well defined hierarchical relation between the two and three--point
correlation functions, remarkably constant with scale. In the angular range
2ββ€ΞΈβ€4β, the southern sample, limited at bIIββ€β40β and including both Abell and ACO clusters, shows a remarkable
hierarchical behavior up to the 6th order, while northern Abell clusters give
positive correlations in the same range only up to the 4th order. The inferred
deprojected values of the 3--D coefficients SJβ, where SJβ=ΞΎΛβJβ/ΞΎΛβ2βJβ1, are similar to those measured for the galaxy
distribution, and consistent with theoretical predictions. These results are
confirmed to the 4th order by our analysis of a 3--D sample of Abell and ACO
clusters. Assuming that selection effects and / or the absence of a cluster
fair sample are the reason of the difference between the two galactic
hemispheres, and between Abell and ACO clusters, our results indicate that the
statistical properties of the cluster distribution originate from the
underlying galaxy distribution and show that the biasing between clusters and
galaxies is non--linear.Comment: 29 pp., (ApJ, accepted for publication). This is a uuencoded
compressed postscript file including figure