Ramsey theory on the integers:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Series: | Student mathematical library
Volume 24 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | xvi, 317 Seiten |
| ISBN: | 0821831992 9780821831991 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
List of Tables xi
Preface xiii
Chapter 1. Preliminaries 1
§1.1. The Pigeonhole Principle 3
§1.2. Ramsey s Theorem 5
§1.3. Some Notation 9
§1.4. Three Classical Theorems 11
§1.5. A Little More Notation 14
§1.6. Exercises 16
§1.7. Research Problems 19
§1.8. References 20
Chapter 2. Van der Waerden s Theorem 21
§2.1. The Compactness Principle 25
§2.2. Alternate Forms of van der Waerden s Theorem 27
§2.3. Computing van der Waerden Numbers 29
vii
viii Contents
§2.4. Bounds on van der Waerden Numbers 35
§2.5. The Erdos and Turan Function 41
§2.6. Proof of van der Waerden s Theorem 43
§2.7. Exercises 49
§2.8. Research Problems 51
§2.9. References 52
Chapter 3. Supersets of AP 55
§3.1. Quasi progressions 56
§3.2. Generalized Quasi progressions 66
§3.3. Descending Waves 70
§3.4. Semi progressions 72
§3.5. Iterated Polynomials 81
§3.6. Arithmetic Progressions as Recurrence Solutions 91
§3.7. Exercises 93
§3.8. Research Problems 96
§3.9. References l00
Chapter 4. Subsets of AP 103
§4.1. Finite Gap Sets 105
§4.2. Infinite Gap Sets 111
§4.3. Exercises 129
§4.4. Research Problems l31
§4.5. References 133
Chapter 5. Other Generalizations of w(k r) 135
§5.1. Sequences of Type ;r, ax + d, bx + 2d 135
§5.2. Homothetic Copies of Sequences 147
Contents ix
§5.3. Sequences of Type x, x + d. x + 2d +b 152
§5.4. Exercises 158
§5.5. Research Problems 159
§5.6. References 160
Chapter 6. Arithmetic Progressions (mod m) 163
§6.1. The Family of Arithmetic Progressions (mod/n) 164
§6.2. A Seemingly Smaller Family is More Regular 167
§6.3. The Degree of Regularity 173
§6.4. Exercises 176
§6.5. Research Problems 178
§6.6. References 180
Chapter 7. Other Variations on van der Waerden s Theorem 181
§7.1. The Function Tm(k) 181
§7.2. Monochromatic Sets a{S + b) 185
§7.3. Having Most Elements Monochromatic 187
§7.4. Permutations Avoiding Arithmetic Progressions 191
§7.5. Exercises 195
§7.6. Research Problems 196
§7.7. References 197
Chapter 8. Schur s Theorem 199
§8.1. The Basic Theorem 200
§8.2. A Generalization of Schur s Theorem 211
§8.3. Refinements of Schur s Theorem 216
§8.4. Exercises 219
§8.5. Research Problems 221
x Contents
§8.6. References 222
Chapter 9. Rado s Theorem 225
§9.1. Rado s Single Equation Theorem 225
§9.2. Some Rado Numbers 239
§9.3. Generalizations of the Single Equation Theorem 249
§9.4. Exercises 255
§9.5. Research Problems 257
§9.6. References 258
Chapter 10. Other Topics 261
§10.1. Folkman s Theorem 261
§10.2. Doublefree Sets 265
§10.3. Diffsequences 266
§10.4. Brown s Lemma 276
§10.5. Patterns in Colorings 279
§10.6. Zero sums 281
§10.7. Exercises 288
§10.8. Research Problems 289
§10.9. References 291
Notation 293
Bibliography 297
Index 315
|
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| id | DE-604.BV019354637 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:58:46Z |
| institution | BVB |
| isbn | 0821831992 9780821831991 |
| language | English |
| lccn | 2003062937 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012818598 |
| oclc_num | 53215841 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-824 DE-703 DE-83 DE-11 DE-188 |
| physical | xvi, 317 Seiten |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| 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=012818598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
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