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  • © 2003

Improved Bonferroni Inequalities via Abstract Tubes

Inequalities and Identities of Inclusion-Exclusion Type

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
  2. 1 Introduction and Overview

    • Klaus Dohmen
    Pages 1-4
  3. 2 Preliminaries

    • Klaus Dohmen
    Pages 5-8
  4. 5 Recursive Schemes

    • Klaus Dohmen
    Pages 44-46
  5. 6 Reliability Applications

    • Klaus Dohmen
    Pages 47-81
  6. Bibliography

    • Klaus Dohmen
    Pages 100-109
  7. Back Matter

    Pages 100-111

About this book

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
  • combinatorics

Bibliographic Information

  • Book Title: Improved Bonferroni Inequalities via Abstract Tubes

  • Book Subtitle: Inequalities and Identities of Inclusion-Exclusion Type

  • Authors: Klaus Dohmen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b13785

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-20025-3Published: 08 October 2003

  • eBook ISBN: 978-3-540-39399-3Published: 05 December 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 122

  • Topics: Discrete Mathematics, Order, Lattices, Ordered Algebraic Structures, Probability Theory

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions