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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
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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