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Improved inclusion-exclusion identities via closure operators

Abstract : 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.
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Klaus Dohmen. Improved inclusion-exclusion identities via closure operators. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2000, 4 (1), pp.61-66. ⟨hal-00958945⟩

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