Discrete Mathematics & Theoretical Computer Science (Dec 2000)

Improved inclusion-exclusion identities via closure operators

  • Klaus Dohmen

Journal volume & issue
Vol. 4, no. 1

Abstract

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Let (A v) v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property. The result generalizes three improvements of the inclusion-exclusion principle as well as Whitney's broken circuit theorem on the chromatic polynomial of a graph.