000 03002nam a22005055i 4500
001 978-3-540-39399-3
003 DE-He213
005 20190213151402.0
007 cr nn 008mamaa
008 150519s2003 gw | s |||| 0|eng d
020 _a9783540393993
_9978-3-540-39399-3
024 7 _a10.1007/b13785
_2doi
050 4 _aQA164-167.2
072 7 _aPBV
_2bicssc
072 7 _aMAT036000
_2bisacsh
072 7 _aPBV
_2thema
082 0 4 _a511.6
_223
100 1 _aDohmen, Klaus.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aImproved Bonferroni Inequalities via Abstract Tubes
_h[electronic resource] :
_bInequalities and Identities of Inclusion-Exclusion Type /
_cby Klaus Dohmen.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2003.
300 _aX, 122 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1826
505 0 _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.
520 _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.
650 0 _aCombinatorics.
650 0 _aAlgebra.
650 0 _aDistribution (Probability theory.
650 1 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
_0http://scigraph.springernature.com/things/product-market-codes/M11124
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540200253
776 0 8 _iPrinted edition:
_z9783662165348
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1826
856 4 0 _uhttps://doi.org/10.1007/b13785
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10495
_d10495