000 | 03002nam a22005055i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/b13785 _2doi |
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050 | 4 | _aQA164-167.2 | |
072 | 7 |
_aPBV _2bicssc |
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_aMAT036000 _2bisacsh |
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_aPBV _2thema |
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082 | 0 | 4 |
_a511.6 _223 |
100 | 1 |
_aDohmen, Klaus. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aX, 122 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1826 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b13785 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c10495 _d10495 |