Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type - Lecture Notes in Mathematics 1826 (Paperback)Klaus Dohmen (author)
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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 Moebius functions.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Number of pages: 122
Weight: 430 g
Dimensions: 235 x 155 x 7 mm
Edition: 2003 ed.
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