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＜電子ブック＞
Improved Bonferroni Inequalities via Abstract Tubes : Inequalities and Identities of Inclusion-Exclusion Type / by Klaus Dohmen
(Lecture Notes in Mathematics. ISSN:16179692 ; 1826)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	X, 122 p : online resource
著者標目	*Dohmen, Klaus author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Algebra LCSH:Probabilities FREE:Discrete Mathematics FREE:Order, Lattices, Ordered Algebraic Structures FREE:Probability Theory
一般注記	1. Introduction and Overview -- 2. Preliminaries -- 3.Bonferroni Inequalities via Abstract Tubes -- 4. Abstract Tubes via Closure and Kernel Operators -- 5. Recursive Schemes -- 6. Reliability Applications -- 7. Combinatorial Applications and Related Topics -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/b13785

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