Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1826)
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Table of contents (8 chapters)
Keywords
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.
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
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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: Combinatorics, Order, Lattices, Ordered Algebraic Structures, Probability Theory and Stochastic Processes