ENGLISH

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

By Klaus Dohmen (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2003
ISBN
3540200258, 9783540200253
DOI
10.1007/b13785
LCC
QA3 .L28 no. 1826,QA295 .L28 no. 1826
Open Library ID
OL3693160M
Language
english
Format
PDF
Filesize
678 kB (694211 bytes)
Series
Lecture Notes in Mathematics 1826
Edition
1
Pages
122\118
Library
Kolxo3
Time added
2010-07-29 05:14:56
Combinatorics; OrderLatticesOrdered Algebraic Structures; Probability Theory a

Description

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.

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