Lecture Notes in Mathematics: Improved Bonferroni Inequalities Via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type (Paperback)

Klaus Dohmen
Springer
 9783540200253
3-540-20025-8

This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp.

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as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Mbius functions.