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Improved Bonferroni Inequalities Via Abstract Tubes

✍ Scribed by Klaus Dohmen

Publisher
Springer
Year
2003
Tongue
English
Leaves
113
Series
Lecture Notes in Mathematics
Edition
1
Category
Library
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✦ Synopsis

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 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 MΓΆbius functions.

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Improved Bonferroni Inequalities via Abs
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