Discrete Mathematics & Theoretical Computer Science, Vol 4, No 1 (2000)

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DMTCS vol 4 no 1 (2000), pp. 61-66

Discrete Mathematics & Theoretical Computer Science


Volume 4 n° 1 (2000), pp. 61-66

author:Klaus Dohmen
title:Improved inclusion-exclusion identities via closure operators
keywords:Inclusion-Exclusion, Sieve Formula, Closure Operator, Convex Geometry, Broken Circuit, Reliability
abstract:Let (A_v)_{v\in 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.
reference: Klaus Dohmen (2000), Improved inclusion-exclusion identities via closure operators, Discrete Mathematics and Theoretical Computer Science 4, pp. 61-66
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Automatically produced on Thu Jun 8 18:21:00 CEST 2000 by novelli