Combinatorial number theory and additive group theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
[2009]
|
| Series: | Advanced courses in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | xi, 330 Seiten Illustrationen 24 cm |
| ISBN: | 9783764389611 9783764389628 |
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MARC
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| 245 | 1 | 0 | |a Combinatorial number theory and additive group theory |c [CRM, Centre de Recerca Matemàtica]. Alfred Geroldinger ; Imre Z. Ruzsa |
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| 650 | 4 | |a Kombinatorische Zahlentheorie - Kongress - Barcelona <2008> | |
| 650 | 4 | |a Additive combinatorics | |
| 650 | 4 | |a Combinatorial number theory | |
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Record in the Search Index
| _version_ | 1804139230829477888 |
|---|---|
| adam_text | CONTENTS FOREWORD I ADDITIVE GROUP THEORY AND NON-UNIQUE FACTORIZATIONS
ALFRED GEROLDINGER 1 INTRODUCTION 3 NOTATION 5 1 BASIC CONCEPTS OF
NON-UNIQUE FACTORIZATIONS 7 1.1 ARITHMETICAL INVARIANTS 9 1.2 KRULL
MONOIDS 13 1.3 TRANSFER PRINCIPLES 16 1.4 MAIN PROBLEMS IN FACTORIZATION
THEORY 20 2 THE DAVENPORT CONSTANT AND FIRST PRECISE ARITHMETICAL
RESULTS 21 2.1 THE DAVENPORT CONSTANT 21 2.2 GROUP ALGEBRAS 24 2.3
ARITHMETICAL INVARIANTS AGAIN 29 3 THE STRUCTURE OF SETS OF LENGTHS 35
3.1 UNIONS OF SETS OF LENGTHS 35 3.2 AHNOST ARITHMETICAL
MULTIPROGRESSIONS 38 3.3 THE CHARACTERIZATION PROBLEM 42 4 ADDITION
THEOREMS AND DIRECT ZERO-SUM PROBLEMS 45 4.1 THE THEOREMS OF KNESER AND
OF KEMPERMAN-SCHERK 45 4.2 ON THE ERDOES-GINZBURG-ZIV CONSTANT S(G) AND
ON SOME OF ITS VARIANTS 48 5 INVERSE ZERO-SUM PROBLEMS AND ARITHMETICAL
CONSEQUENCES 57 5.1 CYCLIC GROUPS 57 5.2 GROUPS OF HIGHER RANK 70
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/990502058 DIGITALISIERT
DURCH VIII CONTENTS 5.3 ARITHMETICAL CONSEQUENCES 75 BIBLIOGRAPHY 79 II
SUMSETS AND STRUCTURE IMRE Z. RUZSA 87 INTRODUCTION 89 NOTATION 91 1
CARDINALITY INEQUALITIES 93 1.1 INTRODUCTION 93 1.2 PLUENNECKE S METHOD
95 1.3 MAGNIFICATION AND DISJOINT PATHS 97 1.4 LAYERED PRODUCT 100 1.5
THE INDEPENDENT ADDITION GRAPH 101 1.6 DIFFERENT SUMMANDS 102 1.7
PLUENNECKE S INEQUALITY WITH A LARGE SUBSET 104 1.8 SUMS AND DIFFERENCES
106 1.9 DOUBLE AND TRIPLE SUMS 109 1.10 A + B AND A + 2B 111 1.11 ON THE
NON-COMMUTATIVE CASE 114 2 STRUCTURE OF SETS WITH FEW SUMS 119 2.1
INTRODUCTION 119 2.2 TORSION GROUPS 122 2.3 FREIMAN ISOMORPHISM AND
SMALL MODEIS 125 2.4 ELEMENTS OF FOURIER ANALYSIS ON GROUPS 128 2.5 BOHR
SETS IN SUMSETS 132 2.6 SOME FACTS FROM THE GEOMETRY OF NUMBERS 134 2.7
A GENERALIZED ARITHMETICAL PROGRESSION IN A BOHR SET 135 2.8 FREIMAN S
THEOREM 138 2.9 ARITHMETIC PROGRESSIONS IN SETS WITH SMALL SUMSET 139 3
LOCATION AND SUMSETS 141 3.1 INTRODUCTION 141 3.2 THE CAUCHY-DAVENPORT
INEQUALITY 142 3.3 KNESER S THEOREM 143 3.4 SUMSETS AND DIAMETER, PART 1
146 3.5 THE IMPACT FUNCTION 147 3.6 ESTIMATES FOR THE IMPACT FUNCTION IN
ONE DIMENSION 149 3. CONTENTS IX 3.9 THE IMPACT FUNCTION AND THE HUELL
VOLUME 157 3.10 THE IMPACT VOLUME 159 3.11 HOVANSKII S THEOREM 163 4
DENSITY 167 4.1 ASYMPTOTIC AND SCHNIRELMANN DENSITY 167 4.2
SCHIRELMANN S INEQUALITY 169 4.3 MANN S THEOREM 171 4.4 SCHNIRELMANN S
THEOREM REVISITED 173 4.5 KNESER S THEOREM, DENSITY FORM 177 4.6 ADDING
A BASIS: ERDOES THEOREM 177 4.7 ADDING A BASIS: PLUENNECKE S THEOREM,
DENSITY FORM 179 4.8 ADDING THE SET OF SQUARES OR PRIMES 182 4.9
ESSENTIAL COMPONENTS 184 5 MEASURE AND TOPOLOGY 185 5.1 INTRODUCTION 185
5.2 RAIKOV S THEOREM AND GENERALIZATIONS 185 5.3 THE IMPACT FUNCTION 187
5.4 MEDITATION ON CONVEXITY AND DIMENSION 188 5.5 TOPOLOGIES ON INTEGERS
191 5.6 THE FINEST COMPACTIFICATION 193 5.7 BANACH DENSITY 194 5.8 THE
DIFFERENCE SET TOPOLOGY 196 EXERCISES 199 BIBLIOGRAPHY 207 III THEMATIC
SEMINARS 211 1 A SURVEY ON ADDITIVE AND MULTIPLICATIVE DECOMPOSITIONS OF
SUMSETS AND OF SHIFTED SETS, CHRISTIAN ELSHOLTZ 213 1.1 INTRODUCTION 213
1.2 PART I 214 1.2.1 MULTIPLICATIVE DECOMPOSITIONS OF SUMSETS 214 1.2.2
MULTIPLICATIVE DECOMPOSITIONS OF SHIFTED SETS 216 1.2.3 SOME BACKGROUND
FROM SIEVE METHODS 217 1.2.4 PROOF OF THEOREM ?? 219 1. CONTENTS 1.3.4
THE CASE OF PRIMES 225 1.3.5 CHAINS OF PRIMES IN ARITHMETIC PROGRESSIONS
226 BIBLIOGRAPHY 229 ON THE DETAILED STRUCTURE OF SETS WITH SMALL
ADDITIVE PROPERTY, GREGORY A. FREIMAN 233 2.1 SMALL DOUBLING 233 2.2
SUMS OF DIFFERENT SETS 237 BIBLIOGRAPHY 239 THE ISOPERIMETRIC METHOD,
YAHYA 0. HAMIDOUNE 241 3.1 UNIVERSAL BOUNDS OF SET PRODUCTS 241 3.2 THE
FROBENIUS PROBLEM 243 3.3 THE Q + /3-THEOREMS 244 3.3.1 DIRECT THEOREMS
244 3.3.2 INVERSE THEOREMS 245 3.4 TORSION-FREE GROUPS: THE
ISOPERIMETRIC APPROACH 246 3.5 THE ISOPERIMETRIC FORMALISM 248 3.6 THE
STRUCTURE OF &-ATOMS 250 BIBLIOGRAPHY 251 ADDITIVE STRUCTURE OF
DIFFERENCE SETS, NORBERT HEGYVAERI 253 4.1 INTRODUCTION 253 4.2 THE CASE
D(A) 255 4.3 AN INTERMEZZO; D(D(A)) IS HIGHLY WELL STRUCTURED 258 4.4
FIRST DIFFERENCE SETS AND BOHR SETS I 258 4.5 RAIMI S THEOREM;
DIFFERENCE SET OF PARTITIONS 261 4.6 FIRST DIFFERENCE SETS AND BOHR SETS
II; F0LNER S THEOREM 263 4.7 APPLICATIONS OF F0LNER THEOREM 263
BIBLIOGRAPHY 265 THE POLYNOMIAL METHOD IN ADDITIVE COMBINATORICS, GYULA
KAROLYI 267 5.1 INTRODUCTION 267 5. CONTENTS XI 6.3 REPRESENTATION
FUNCTIONS 280 6.4 SETS WITH MORE SUMS THAN DIFFERENCES 282 6.5
COMPARATIVE THEORY OF LINEAR FORMS 284 6.6 THE FUNDAMENTAL THEOREM OF
ADDITIVE NUMBER THEORY 286 6.7 THIN ASYMPTOTIC BASES 287 6.8 MINIMAL
ASYMPTOTIC BASES 288 6.9 MAXIMAL ASYMPTOTIC NON-BASES 289 6.10
COMPLEMENTING SETS OF INTEGERS 290 6.11 THE CACCETTA-HAEGGKVIST
CONJECTURE 293 BIBLIOGRAPHY 295 7 INDDENCES AND THE SPECTRA OF GRAPHS,
JOZSEF SOLYMOSI 299 7.1 INTRODUCTION 299 7.2 THE SUM-PRODUCT PROBLEM 300
7.2.1 THE SUM-PRODUCT GRAPH 301 7.2.2 THE SPECTRAL BOUND 303 7.3
THREE-TERM ARITHMETIC PROGRESSIONS 304 7.3.1 THE 3-AP GRAPH 304 7.4
SIDON FUNCTIONS 306 7.4.1 SIDON FUNCTIONS 306 7.4.2 A BIPARTITE
INCIDENCE GRAPH 308 7.4.3 THE SPECTRAL BOUND 309 7.5 INCIDENCE BOUNDS ON
PSEUDOLINES 310 7.5.1 THE INCIDENCE BOUND 310 7.5.2 STRONGLY REGULAER
GRAPHS 311 BIBLIOGRAPHY 313 8 MULTI-DIMENSIONAL INVERSE ADDITIVE
PROBLEMS, YONUTZ V. STANCHESCU 315 8.1 DIRECT AND INVERSE PROBLEMS OF
ADDITIVE AND COMBINATORIAL NUMBER THEORY 315 8.2 THE SIMPLEST INVERSE
PROBLEM FOR SUMS OF SETS IN SEVERAL DIMENSIONS 316 8.3 SMALL DOUBLING
PROPERTY ON THE PLANE 318 8.4 PLANAR SETS WITH NO THREE COLLINEAR POINTS
ON A LINE 321 8.
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 511 - General principles of mathematics |
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| discipline | Mathematik |
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| id | DE-604.BV035575406 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:40:47Z |
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| isbn | 9783764389611 9783764389628 |
| language | English |
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| spelling | Geroldinger, Alfred 1961- (DE-588)131835807 aut Combinatorial number theory and additive group theory [CRM, Centre de Recerca Matemàtica]. Alfred Geroldinger ; Imre Z. Ruzsa Basel ; Boston ; Berlin Birkhäuser [2009] © 2009 xi, 330 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Advanced courses in mathematics Literaturangaben Kombinatorische Zahlentheorie - Kongress - Barcelona <2008> Additive combinatorics Combinatorial number theory Kombinatorische Zahlentheorie (DE-588)4164751-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2008 Barcelona gnd-content Kombinatorische Zahlentheorie (DE-588)4164751-8 s DE-604 Ruzsa, Imre 1921-2008 (DE-588)119285894 aut Centre de Recerca Matemàtica Sonstige (DE-588)10029789-4 oth Erscheint auch als Online-Ausgabe 978-3-7643-8962-8 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017630909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Geroldinger, Alfred 1961- Ruzsa, Imre 1921-2008 Combinatorial number theory and additive group theory Kombinatorische Zahlentheorie - Kongress - Barcelona <2008> Additive combinatorics Combinatorial number theory Kombinatorische Zahlentheorie (DE-588)4164751-8 gnd |
| subject_GND | (DE-588)4164751-8 (DE-588)1071861417 |
| title | Combinatorial number theory and additive group theory |
| title_auth | Combinatorial number theory and additive group theory |
| title_exact_search | Combinatorial number theory and additive group theory |
| title_full | Combinatorial number theory and additive group theory [CRM, Centre de Recerca Matemàtica]. Alfred Geroldinger ; Imre Z. Ruzsa |
| title_fullStr | Combinatorial number theory and additive group theory [CRM, Centre de Recerca Matemàtica]. Alfred Geroldinger ; Imre Z. Ruzsa |
| title_full_unstemmed | Combinatorial number theory and additive group theory [CRM, Centre de Recerca Matemàtica]. Alfred Geroldinger ; Imre Z. Ruzsa |
| title_short | Combinatorial number theory and additive group theory |
| title_sort | combinatorial number theory and additive group theory |
| topic | Kombinatorische Zahlentheorie - Kongress - Barcelona <2008> Additive combinatorics Combinatorial number theory Kombinatorische Zahlentheorie (DE-588)4164751-8 gnd |
| topic_facet | Kombinatorische Zahlentheorie - Kongress - Barcelona <2008> Additive combinatorics Combinatorial number theory Kombinatorische Zahlentheorie Konferenzschrift 2008 Barcelona |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017630909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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