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

• Main Author: Dohmen, Klaus (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1826
• Subjects: Combinatorics.; Algebra.; Ordered algebraic structures.; Probabilities.; Order, Lattices, Ordered Algebraic Structures.; Probability Theory and Stochastic Processes.

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...

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.