Ramsey theory on the integers:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Edition: | Second edition |
| Series: | Student mathematical library
volume 73 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027937221&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverzeichnis: Seite 357 - 380 |
| Physical Description: | xx, 384 Seiten |
| ISBN: | 9780821898673 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Titel: Ramsey theory on the integers
Autor: Landman, Bruce M
Jahr: 2014
Contents
List of Tables xi
Preface to the Second Edition xiii
Acknowledgements xv
Preface to the First Edition xvii
Chapter 1. Preliminaries 1
§1.1. The Pigeonhole Principle 3
§1.2. Ramsey s Theorem 6
§1.3. Some Notation 9
§1.4. Three Classical Theorems 11
§1.5. A Little More Notation 14
§1.6. Exercises 17
§1.7. Research Problems 20
§1.8. References 21
Chapter 2. Van der Waerden s Theorem 23
§2.1. The Compactness Principle 27
§2.2. Alternate Forms of van der Waerden s Theorem 29
§2.3. Computing van der Waerden Numbers 31
vii
viii
Contents
§2.4. Bounds »Ii van der Warnten Numhers 3*
§2.5. The Erdös and Turan Function 17
§2.6. ()n t.he Number of Monnrhnunatie Arithmetie
Progressions 51
§2.7. Proof of van der Waerdcn s Theorem 54
§2.8. Exercises 57
§2.9. Research Problems 59
§2.10. References (12
Chapter 3. Supersets of AI (17
§3.1. Quasi-Progressions (iS
§3.2. Generali/,cd Quasi-Progressions 77
§3.3. Oeseeudtne Waves S1
§3.4. Semi-Progressions 83
§3.5. lt.erat.ed Polynomials 92
§3.6. Arithmetk Progressions as Reeurrenee Solutions 102
§3.7. Exercises |(M
§3.8. Research Problems 107
§3.9. References 111
Chapter 4. Subsets of .4/ 14
§4.1. Finit.e Gap Sets 115
§4.2. Infinite Gap Sets 121
§4.3. Exercises 140
§4.4. Research Problems 142
§4.5. References 145
Chapter 5. Othcr Generalizatioris of w(k: r) 147
§5.1. Sequences of Type ,r. ax + 1. + 2ii 147
§5.2. Homothetic Copies of Sequetires 163
§5.3. Se iuences of Type x, x + ,/. x f 2,1 t h 168
§5.4. Polynomial Progressions 175
§5.5. Exercises 177
Contents
ix
§5.6. Research Problems 17b
§5.7. References IM
Chapter 0. Arithmetic Progressions Iniiidm) 1*3
§6. 1. The Family of Arithmetic Progressions (niodm) 1*4
§6.2. A Scemingly Smaller Family is More Regulär 1*7
§6.3. I lie Degree of Regularity 193
§6.4. Kxereises 196
§6.5. Research Problems 19*
§6.6. References 200
Chapter 7. Othcr Variations on van der Waerden s Theorem 203
§7.1. The Function rjr,(A-) 203
§7.2. Monochromatic Sets o(S + b) 207
§7.3. Having Most Elements Monochromatic 209
§7.4. Pernmtations Avoiding Arithmetic Progressions 213
§7.7). Exercises 217
§7.6. Research Problems 217
§7.7. References 219
Chapter 8. Schur s Theorem 221
§8.1. The Basic Theorem 222
§8.2. A Gcnera.lization of Schur s Theorem 234
§8.3. Refinements of Schur s Theorem 239
§8.4. Schur Ineqtiality 243
§8.5. Exercises 245
§8.6. Research Problems 247
§8.7. References 248
Chapter 9. Rado s Theorem 251
§9.1. Rado s Single Equation Theorem 251
§9/2. Sonic Rado Ntnnbers 2 S
§9.3. Generalizatiotis of the Single Equation 1 hörnern 279
X
Contents
§9.4. Solutions to Linear Recurrences 285
§9.5. Mixing Addition and Multiplication 287
§9.6. Exercises 290
§9.7. Research Problems 292
§9.8. References 294
Chapter 10. Other Topics 297
§10.1. Monochromatic Sums 297
§10.2. Doublefree Sets 302
§10.3. Diffsequences 303
§10.4. Brown s Lemma 318
§10.5. Monochromatic Sets Free of Prescribed Differences 321
§10.6. Patterns in Colorings 326
§10.7. Rainbow Ramsey Theory on the Integers 328
§10.8. Zero-Sums and m-Sets 334
§10.9. Exercises 345
§10.10. Research Problems 346
§10.11. References 349
Notation 353
Bibliography 357
Index 381
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV042502525 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:12:58Z |
| institution | BVB |
| isbn | 9780821898673 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027937221 |
| oclc_num | 915643891 |
| open_access_boolean | |
| owner | DE-83 DE-188 DE-20 DE-11 |
| owner_facet | DE-83 DE-188 DE-20 DE-11 |
| physical | xx, 384 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spellingShingle | Landman, Bruce M. 1951- Robertson, Aaron 1971- Ramsey theory on the integers Student mathematical library Ramsey, Théorie de Ramsey theory Ramsey-Theorie (DE-588)4212682-4 gnd |
| subject_GND | (DE-588)4212682-4 |
| title | Ramsey theory on the integers |
| title_auth | Ramsey theory on the integers |
| title_exact_search | Ramsey theory on the integers |
| title_full | Ramsey theory on the integers Bruce M. Landman ; Aaron Robertson |
| title_fullStr | Ramsey theory on the integers Bruce M. Landman ; Aaron Robertson |
| title_full_unstemmed | Ramsey theory on the integers Bruce M. Landman ; Aaron Robertson |
| title_short | Ramsey theory on the integers |
| title_sort | ramsey theory on the integers |
| topic | Ramsey, Théorie de Ramsey theory Ramsey-Theorie (DE-588)4212682-4 gnd |
| topic_facet | Ramsey, Théorie de Ramsey theory Ramsey-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027937221&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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