Description

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 Möbius functions.

Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type

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Paperback / softback by Klaus Dohmen

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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,... Read more

    Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
    Publication Date: 08/10/2003
    ISBN13: 9783540200253, 978-3540200253
    ISBN10: 3540200258

    Number of Pages: 122

    Non Fiction , Mathematics & Science , Education

    Description

    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 Möbius functions.

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