Absolute bounds on set intersection and union sizes from distribution information

A catalog of quick closed-form bounds on set intersection and union sizes is presented; they can be expressed as rules, and managed by a rule-based system architecture. These methods use a variety of statistics precomputed on the data, and exploit homomorphisms (onto mappings) of the data items onto distributions that can be more easily analyzed. The methods can be used anytime, but tend to work best when there are strong or complex correlations in the data. This circumstance is poorly handled by the standard independence-assumption and distributional-assumption estimates