Inclusion-Exclusion(3) Implies Inclusion-Exclusion(n)
Devdatt Dubhashi · BRICS Report Series · 1995
We consider a natural generalisation of the familiar inclusion-exclusion formula for sets in the setting of ranked lattices. We show that the generalised inclusion-exclusion formula holds in a lattice if and only if the lattice is distributive and the rank function is modular. As a consequence it turns out (perhaps surprisingly) that the inclusion-exclusion formula for three elements implies the inclusion-exclusion formula for an arbitrary number of elements.