03560nam 22006975 450 991014462070332120230617035935.03-540-39399-410.1007/b13785(CKB)1000000000230799(SSID)ssj0000323928(PQKBManifestationID)11245091(PQKBTitleCode)TC0000323928(PQKBWorkID)10305112(PQKB)11364110(DE-He213)978-3-540-39399-3(MiAaPQ)EBC6299080(MiAaPQ)EBC5585524(Au-PeEL)EBL5585524(OCoLC)166469097(EXLCZ)99100000000023079920150519d2003 u| 0engurnn|008mamaatxtccrImproved Bonferroni Inequalities via Abstract Tubes Inequalities and Identities of Inclusion-Exclusion Type /by Klaus Dohmen1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (X, 122 p.) Lecture Notes in Mathematics,0075-8434 ;1826Based on author's habilitation thesis--Humboldt-University.3-540-20025-8 Includes bibliographical references and indexes.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.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.Lecture Notes in Mathematics,0075-8434 ;1826Combinatorial analysisAlgebraOrdered algebraic structuresProbabilitiesCombinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Order, Lattices, Ordered Algebraic Structureshttps://scigraph.springernature.com/ontologies/product-market-codes/M11124Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Combinatorial analysis.Algebra.Ordered algebraic structures.Probabilities.Combinatorics.Order, Lattices, Ordered Algebraic Structures.Probability Theory and Stochastic Processes.512.97Dohmen Klausauthttp://id.loc.gov/vocabulary/relators/aut149982MiAaPQMiAaPQMiAaPQBOOK9910144620703321Improved Bonferroni inequalities via abstract tubes168037UNINA