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

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 grap...

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Bibliographic Details
Main Author: Dohmen, Klaus
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2003, 2003
Edition:1st ed. 2003
Series:Lecture Notes in Mathematics
Subjects:
Probability Theory
Algebra
Discrete Mathematics
Order, Lattices, Ordered Algebraic Structures
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Improved Bonferroni Inequalities via Abstract Tubes  |h Elektronische Ressource  |b Inequalities and Identities of Inclusion-Exclusion Type  |c by Klaus Dohmen 
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505 0 |a 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 
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653 |a Discrete Mathematics 
653 |a Order, Lattices, Ordered Algebraic Structures 
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653 |a Probabilities 
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520 |a 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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