Inclusion-exclusion enhanced by nerve stimulation

Abstract

When evaluating the lengthy inclusion-exclusion expansion many of its terms may turn out to be zero, and hence should be discarded beforehand. Often this can be done. The main idea is that the index sets of nonzero terms constitute a set ideal (called the 'nerve'), which often can be encoded in a compact way (Upgrade B). As a further enhancement (Upgrade A), equal nonzero terms can sometimes be efficiently collected.