Improved Bonferroni Inequalities via Abstract Tubes

Inequalities and Identities of Inclusion-Exclusion Type

  • Authors
  • Klaus Dohmen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1826)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Klaus Dohmen
    Pages 1-4
  3. Klaus Dohmen
    Pages 5-8
  4. Klaus Dohmen
    Pages 44-46
  5. Klaus Dohmen
    Pages 47-81
  6. Klaus Dohmen
    Pages 100-109
  7. Back Matter
    Pages 100-111

About this book

Introduction

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.

Keywords

Bonferroni inequalities Graph theory Lattice abstract tube graph sieve inclusion-exclusion matroid network

Bibliographic information

  • DOI https://doi.org/10.1007/b13785
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20025-3
  • Online ISBN 978-3-540-39399-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book