Improved Bonferroni inequalities via abstract tubes: inequalities and identities of inclusion-exclusion type
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Lecture notes in mathematics
1826 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 109 S. graph. Darst. : 24 cm |
| ISBN: | 3540200258 |
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| 100 | 1 | |a Dohmen, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Improved Bonferroni inequalities via abstract tubes |b inequalities and identities of inclusion-exclusion type |c Klaus Dohmen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction and Overview 1
2 Preliminaries 5
2.1 Graphs and posets 5
2.2 Topology 7
3 Bonferroni Inequalities via Abstract Tubes 9
3.1 An outline of abstract tube theory 9
3.1.1 The notion of an abstract tube 9
3.1.2 Two fundamental theorems on abstract tubes 11
3.1.3 An importance sampling scheme 13
3.2 Examples of abstract tubes 14
3.2.1 Abstract tubes for convex polyhedra 14
3.2.2 Abstract tubes for unions of balls and spherical caps ... 15
4 Abstract Tubes via Closure and Kernel Operators 19
4.1 Abstract tubes via closure operators 19
4.1.1 Closure operators 19
4.1.2 How closure operators lead to abstract tubes 21
4.2 Abstract tubes via kernel operators 25
4.2.1 Kernel operators 25
4.2.2 How kernel operators lead to abstract tubes 26
4.3 Alternative proofs 28
4.3.1 Improved identities via closure operators 28
4.3.2 Improved inequalities via kernel operators 33
4.3.3 Additional proofs of identities 35
4.4 The chordal graph sieve 37
5 Recursive Schemes 44
5.1 Recursive schemes for semilattices 44
5.2 Dynamic programming approach 45
VIII Contents
6 Reliability Applications 47
6.1 System reliability 47
6.1.1 Terminology 47
6.1.2 Abstract tubes for system reliability 48
6.1.3 Shier s pseudopolynomial algorithm 49
6.1.4 Inclusion exclusion and domination theory 52
6.2 Special reliability systems 53
6.2.1 Communications networks 53
6.2.2 fc out of n systems 66
6.2.3 Consecutive /c out of n systems 70
6.3 Reliability covering problems 75
6.3.1 The hypergraph model 75
6.3.2 Abstract tubes and polynomial algorithms 75
6.4 Chapter notes 81
7 Combinatorial Applications and Related Topics 82
7.1 Inclusion exclusion on partition lattices 82
7.2 Chromatic polynomials and broken circuits 83
7.2.1 The usual chromatic polynomial 84
7.2.2 The generalized chromatic polynomial 86
7.3 Sums over partially ordered sets 89
7.3.1 A general theorem on sums 89
7.3.2 Application to inclusion exclusion 90
7.4 Matroid polynomials and the (3 invariant 91
7.4.1 The Tutte polynomial 91
7.4.2 The characteristic polynomial 93
7.4.3 The (3 invariant 94
7.5 Euler characteristics and Mobius functions 95
7.5.1 Euler characteristics 95
7.5.2 Mobius functions 96
Bibliography 100
Author Index 111
Subject Index 113
|
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| dewey-full | 510S512.9/722 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-sort | 3510 S 3512.9 17 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| isbn | 3540200258 |
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| physical | VIII, 109 S. graph. Darst. : 24 cm |
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| spelling | Dohmen, Klaus Verfasser aut Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type Klaus Dohmen Berlin [u.a.] Springer 2003 VIII, 109 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1826 Zugl.: Berlin, Humboldt-Univ., Habil.-Schr. Analyse combinatoire Analyse combinatoire ram Distribution (Théorie des probabilités) Inégalités (Mathématiques) Inégalités (mathématiques) ram Probabilités combinatoires Inequalities (Mathematics) Distribution (Probability theory) Combinatorial analysis Combinatorial probabilities Bonferroni-Ungleichung (DE-588)4426106-8 gnd rswk-swf Inklusions-Exklusions-Prinzip (DE-588)4637190-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bonferroni-Ungleichung (DE-588)4426106-8 s Inklusions-Exklusions-Prinzip (DE-588)4637190-4 s DE-604 Lecture notes in mathematics 1826 (DE-604)BV000676446 1826 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537683&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dohmen, Klaus Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type Lecture notes in mathematics Analyse combinatoire Analyse combinatoire ram Distribution (Théorie des probabilités) Inégalités (Mathématiques) Inégalités (mathématiques) ram Probabilités combinatoires Inequalities (Mathematics) Distribution (Probability theory) Combinatorial analysis Combinatorial probabilities Bonferroni-Ungleichung (DE-588)4426106-8 gnd Inklusions-Exklusions-Prinzip (DE-588)4637190-4 gnd |
| subject_GND | (DE-588)4426106-8 (DE-588)4637190-4 (DE-588)4113937-9 |
| title | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type |
| title_auth | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type |
| title_exact_search | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type |
| title_full | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type Klaus Dohmen |
| title_fullStr | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type Klaus Dohmen |
| title_full_unstemmed | Improved Bonferroni inequalities via abstract tubes inequalities and identities of inclusion-exclusion type Klaus Dohmen |
| title_short | Improved Bonferroni inequalities via abstract tubes |
| title_sort | improved bonferroni inequalities via abstract tubes inequalities and identities of inclusion exclusion type |
| title_sub | inequalities and identities of inclusion-exclusion type |
| topic | Analyse combinatoire Analyse combinatoire ram Distribution (Théorie des probabilités) Inégalités (Mathématiques) Inégalités (mathématiques) ram Probabilités combinatoires Inequalities (Mathematics) Distribution (Probability theory) Combinatorial analysis Combinatorial probabilities Bonferroni-Ungleichung (DE-588)4426106-8 gnd Inklusions-Exklusions-Prinzip (DE-588)4637190-4 gnd |
| topic_facet | Analyse combinatoire Distribution (Théorie des probabilités) Inégalités (Mathématiques) Inégalités (mathématiques) Probabilités combinatoires Inequalities (Mathematics) Distribution (Probability theory) Combinatorial analysis Combinatorial probabilities Bonferroni-Ungleichung Inklusions-Exklusions-Prinzip Hochschulschrift |
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