Inclusion-Exclusion(3) Implies Inclusion-Exclusion(n)

Devdatt P. Dubhashi

February 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.

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