Lectures on advances in combinatorics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2008
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 291 - 305 |
| Physical Description: | XIII, 314 S. 24 cm, 470 gr. |
| ISBN: | 9783540786016 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lectures on advances in combinatorics |c Rudolf Ahlswede ; Vladimir Blinovsky |
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Record in the Search Index
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| adam_text | Table of Contents
Chapter I Conventions and Auxiliary Results 1
Chapter II Intersection and Diametric Problems 9
Lecture 1 The Complete Intersection Theorem 9
Lecture 2 The Diametric Problem for Vertices in the Hamming Metric 18
Lecture 3 The Diametric Problem for Vertices in the Taxi Metric 30
Lecture 4 The Diametric Problem for Kdges in Hamming Metric 41
Lecture 5 Words with Pairwise Common Letter 49
§1 Asymptotical Behavior of g^ 50
Lecture 6 Constant Distance Code Pairs 52
§ 1 The Exact Value of Mq(n.S) 52
§2 Four-Words Property 64
Chapter III Covering, Packing, and List Codes 73
Lecture 7 Covering and Packing of Hypergraphs 73
Lecture 8 Covering of Products of Graphs and Hypergraphs 83
Lecture 9 Multiple Packing 89
§ 1 A Lower Bound 91
§2 An Upper Bound for Rq.L{p) 94
§3 An Upper Bound for/? ,x(t) 98
xii Table of Contents
Lecture 10 List Decoding 105
§ 1 The Exponent of List-of-L Decoding Error Probability at Zero Rate 109
§2 The Expurgation Bound 118
Chapter IV Higher Level and Dimension Constrained
Extremal Problems 125
Lecture 11 Higher Level Extremal Problems 125
§1 The Asymptotics of the Numbers Dn(3,V,k), Dn(V,3,k)
andDn(3,3,k) 126
§2 Other Cases of Higher Level Extremal Problems 129
Lecture 12 Properties of Binary Sequences Over Reals 135
§ 1 The Size of Positive Linear Combinations Free Sets 136
§2 The Unit Cube in the Euclidean Space 140
§3 /^-Dimensional Sets of Binary Vectors of Given Weight 141
Chapter V LYM-Related AZ-Identities, Antichain Splittings
and Correlation Inequalities 151
Lecture 13 LYM-Type Relations 151
§ 1 The AZ-Identity and Related Results 152
Lecture 14 The Splitting Property 158
§ 1 Antichains that Satisfy the Splitting Condition 159
Lecture 15 Correlation Inequalities l°0
§1 AD Inequality 162
§2 Other Boolean Operations 1°8
§3 Arithmetical Operations 171
§4 Implications for Order Extensions and Random Permutations 173
§5 General Correlation Inequalities: Methods for Proving Them 175
§6 Number Theoretical Correlation Inequalities 182
Chapter VI Basic Problems from Combinatorial Number Theory 199
Lecture 16 Solutions of Problems of P. Erdos 199
§1 Definitions, Formulation of Problems, and Conjectures 199
§2 Auxiliary Results: New Combinatorial and Known Number
Theoretical Properties 200
§3 Maximal Sets Without k + 1 Coprimes 205
§4 Proof of the Main Result 208
§5 Maximal Sets Without Coprimes 217
§6 Counterexamples for Small n 222
Table of Contents iii
Appendix 225
References 291
Index 307
List of Symbols 311
|
| adam_txt |
Table of Contents
Chapter I Conventions and Auxiliary Results 1
Chapter II Intersection and Diametric Problems 9
Lecture 1 The Complete Intersection Theorem 9
Lecture 2 The Diametric Problem for Vertices in the Hamming Metric 18
Lecture 3 The Diametric Problem for Vertices in the Taxi Metric 30
Lecture 4 The Diametric Problem for Kdges in Hamming Metric 41
Lecture 5 Words with Pairwise Common Letter 49
§1 Asymptotical Behavior of g^ 50
Lecture 6 Constant Distance Code Pairs 52
§ 1 The Exact Value of Mq(n.S) 52
§2 Four-Words Property 64
Chapter III Covering, Packing, and List Codes 73
Lecture 7 Covering and Packing of Hypergraphs 73
Lecture 8 Covering of Products of Graphs and Hypergraphs 83
Lecture 9 Multiple Packing 89
§ 1 A Lower Bound 91
§2 An Upper Bound for Rq.L{p) 94
§3 An Upper Bound for/? ,x(t) 98
xii Table of Contents
Lecture 10 List Decoding 105
§ 1 The Exponent of List-of-L Decoding Error Probability at Zero Rate 109
§2 The Expurgation Bound 118
Chapter IV Higher Level and Dimension Constrained
Extremal Problems 125
Lecture 11 Higher Level Extremal Problems 125
§1 The Asymptotics of the Numbers Dn(3,V,k), Dn(V,3,k)
andDn(3,3,k) 126
§2 Other Cases of Higher Level Extremal Problems 129
Lecture 12 Properties of Binary Sequences Over Reals 135
§ 1 The Size of Positive Linear Combinations Free Sets 136
§2 The Unit Cube in the Euclidean Space 140
§3 /^-Dimensional Sets of Binary Vectors of Given Weight 141
Chapter V LYM-Related AZ-Identities, Antichain Splittings
and Correlation Inequalities 151
Lecture 13 LYM-Type Relations 151
§ 1 The AZ-Identity and Related Results 152
Lecture 14 The Splitting Property 158
§ 1 Antichains that Satisfy the Splitting Condition 159
Lecture 15 Correlation Inequalities l°0
§1 AD Inequality 162
§2 Other Boolean Operations 1°8
§3 Arithmetical Operations 171
§4 Implications for Order Extensions and Random Permutations 173
§5 General Correlation Inequalities: Methods for Proving Them 175
§6 Number Theoretical Correlation Inequalities 182
Chapter VI Basic Problems from Combinatorial Number Theory 199
Lecture 16 Solutions of Problems of P. Erdos 199
§1 Definitions, Formulation of Problems, and Conjectures 199
§2 Auxiliary Results: New Combinatorial and Known Number
Theoretical Properties 200
§3 Maximal Sets Without k + 1 Coprimes 205
§4 Proof of the Main Result 208
§5 Maximal Sets Without Coprimes 217
§6 Counterexamples for Small n 222
Table of Contents "iii
Appendix 225
References 291
Index 307
List of Symbols 311 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ahlswede, Rudolf 1938-2010 Blinovskij, Vladimir M 1959- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 890 |
| ctrlnum | (OCoLC)222164335 (DE-599)DNB989061841 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035133016 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:25:05Z |
| indexdate | 2024-07-09T21:23:04Z |
| institution | BVB |
| isbn | 9783540786016 |
| language | English |
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| physical | XIII, 314 S. 24 cm, 470 gr. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Ahlswede, Rudolf 1938-2010 Verfasser (DE-588)121242293 aut Lectures on advances in combinatorics Rudolf Ahlswede ; Vladimir Blinovsky Berlin ; Heidelberg Springer 2008 XIII, 314 S. 24 cm, 470 gr. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 291 - 305 Combinatorial analysis Extremalproblem (DE-588)4439315-5 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Extremalproblem (DE-588)4439315-5 s DE-604 Blinovskij, Vladimir M 1959- Verfasser (DE-588)122147170 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016800505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ahlswede, Rudolf 1938-2010 Blinovskij, Vladimir M 1959- Lectures on advances in combinatorics Combinatorial analysis Extremalproblem (DE-588)4439315-5 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4439315-5 (DE-588)4031824-2 |
| title | Lectures on advances in combinatorics |
| title_auth | Lectures on advances in combinatorics |
| title_exact_search | Lectures on advances in combinatorics |
| title_exact_search_txtP | Lectures on advances in combinatorics |
| title_full | Lectures on advances in combinatorics Rudolf Ahlswede ; Vladimir Blinovsky |
| title_fullStr | Lectures on advances in combinatorics Rudolf Ahlswede ; Vladimir Blinovsky |
| title_full_unstemmed | Lectures on advances in combinatorics Rudolf Ahlswede ; Vladimir Blinovsky |
| title_short | Lectures on advances in combinatorics |
| title_sort | lectures on advances in combinatorics |
| topic | Combinatorial analysis Extremalproblem (DE-588)4439315-5 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Combinatorial analysis Extremalproblem Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016800505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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