Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type / Edition 1

Improved Bonferroni Inequalities via Abstract Tubes: Inequalities and Identities of Inclusion-Exclusion Type / Edition 1

by Klaus Dohmen
     
 

ISBN-10: 3540200258

ISBN-13: 9783540200253

Pub. Date: 12/05/2003

Publisher: Springer Berlin Heidelberg

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

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Overview

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.

Product Details

ISBN-13:
9783540200253
Publisher:
Springer Berlin Heidelberg
Publication date:
12/05/2003
Series:
Lecture Notes in Mathematics Series, #1826
Edition description:
2003
Pages:
122
Product dimensions:
6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

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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