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100   $a20150519d2003      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aImproved Bonferroni Inequalities via Abstract Tubes$b[electronic resource] $eInequalities and Identities of Inclusion-Exclusion Type /$fby Klaus Dohmen
205   $a1st ed. 2003.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003.
215   $a1 online resource (X, 122 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1826
300   $aBased on author's habilitation thesis--Humboldt-University.
311   $a3-540-20025-8 
320   $aIncludes bibliographical references and indexes.
327   $a1. 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.
330   $aThis introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1826
606   $aCombinatorics
606   $aAlgebra
606   $aOrdered algebraic structures
606   $aProbabilities
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
606   $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
615  0$aCombinatorics.
615  0$aAlgebra.
615  0$aOrdered algebraic structures.
615  0$aProbabilities.
615 14$aCombinatorics.
615 24$aOrder, Lattices, Ordered Algebraic Structures.
615 24$aProbability Theory and Stochastic Processes.
676   $a512.97
700   $aDohmen$b Klaus$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149982
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466478403316
996   $aImproved Bonferroni inequalities via abstract tubes$9168037
997   $aUNISA