Ramsey theory:
"Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction be...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1990
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley-Interscience series in discrete mathematics and optimization
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms." -- Book cover. |
| Beschreibung: | XI, 196 S. graph. Darst. |
| ISBN: | 0471500461 |
Internformat
MARC
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| 245 | 1 | 0 | |a Ramsey theory |c Ronald L. Graham ; Bruce L. Rothschild ; Joel H. Spencer |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1990 | |
| 300 | |a XI, 196 S. |b graph. Darst. | ||
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| 490 | 0 | |a Wiley-Interscience series in discrete mathematics and optimization | |
| 490 | 0 | |a A Wiley-Interscience publication | |
| 520 | 3 | |a "Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms." -- Book cover. | |
| 650 | 4 | |a Ramsey, Théorie de | |
| 650 | 7 | |a Ramsey, théorie de |2 ram | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Ramsey theory | |
| 650 | 0 | 7 | |a Ramsey-Theorie |0 (DE-588)4212682-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1808860911594635264 |
|---|---|
| adam_text |
Contents
Notation xi
1 Sets 1
1.1 Ramsey's Theorem Abridged 1
1.2 Ramsey's Theorem Unabridged 7
1.3 Views of Ramsey Theory 9
1.4 Ramsey Theorems and Density Theorems 12
1.5 The Compactness Principle 13
1.6 A Broader Perspective 17
1.7 Original Papers: Ramsey and Erdos Szekeres 18
Remarks and References 26
2 Progressions 29
2.1 Van der Waerden's Theorem 29
2.2 The Hales Jewett Theorem 34
2.3 Extensions and Implications 40
2.4 Spaces—Affine and Vector 42
2.5 Roth's Theorem and Szemeredi's Theorem 45
2.6 The Shelah Proof 54
2.7 Eeeeenormous Upper Bounds 60
Remarks and References 68
3 Equations 69
3.1 Schur's Theorem 69
3.2 Regular Homogeneous Equations (Rado's Theorem—
Abridged) 71
3.3 Regular Homogeneous Systems (Rado's Theorem
Complete) 73
3.4 Finite Sums and Finite Unions (Folkman's Theorem) 81
ix
x Contents
3.5 Infinite Sets of Sums (Hindman's Theorem) 84
3.6 Regular Nonhomogeneous Systems 87
Remarks and References 88
4 Numbers 89
4.1 Ramsey Numbers—Exact 89
4.2 Ramsey Numbers—Asymptotics 92
4.3 Van der Waerden Numbers 96
4.4 The Symmetric Hypergraph Theorem 99
4.5 Schur and Rado Numbers 103
4.6 Property B 104
4.7 Higher Ramsey Numbers 106
Remarks and References 109
5 Particulars 111
5.1 Bipartite Ramsey Theorems 111
5.2 Induced Ramsey Theorems 114
5.3 Restricted Ramsey Results 119
5.4 Equations over Abelian Groups 123
5.5 Canonical Ramsey Theorems 129
5.6 Euclidean Ramsey Theory 133
5.7 Graph Ramsey Theory 138
6 Beyond Combinatorics 153
6.1 Topological Dynamics 153
6.2 Ultrafilters 166
6.3 An Unprovable Theorem 169
6.4 The Infinite 180
References 187
Index 193 |
| any_adam_object | 1 |
| author | Graham, Ronald L. 1935-2020 Rothschild, Bruce L. 1941- Spencer, Joel H. 1946- |
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| ctrlnum | (OCoLC)20294861 (DE-599)BVBBV006345494 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV006345494 |
| illustrated | Illustrated |
| indexdate | 2024-08-31T00:29:53Z |
| institution | BVB |
| isbn | 0471500461 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004015517 |
| oclc_num | 20294861 |
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| physical | XI, 196 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics and optimization A Wiley-Interscience publication |
| spelling | Graham, Ronald L. 1935-2020 Verfasser (DE-588)132783843 aut Ramsey theory Ronald L. Graham ; Bruce L. Rothschild ; Joel H. Spencer 2. ed. New York [u.a.] Wiley 1990 XI, 196 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization A Wiley-Interscience publication "Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms." -- Book cover. Ramsey, Théorie de Ramsey, théorie de ram Combinatorial analysis Ramsey theory Ramsey-Theorie (DE-588)4212682-4 gnd rswk-swf Ramsey-Theorie (DE-588)4212682-4 s DE-604 Rothschild, Bruce L. 1941- Verfasser (DE-588)1279097191 aut Spencer, Joel H. 1946- Verfasser (DE-588)133091546 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004015517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graham, Ronald L. 1935-2020 Rothschild, Bruce L. 1941- Spencer, Joel H. 1946- Ramsey theory Ramsey, Théorie de Ramsey, théorie de ram Combinatorial analysis Ramsey theory Ramsey-Theorie (DE-588)4212682-4 gnd |
| subject_GND | (DE-588)4212682-4 |
| title | Ramsey theory |
| title_auth | Ramsey theory |
| title_exact_search | Ramsey theory |
| title_full | Ramsey theory Ronald L. Graham ; Bruce L. Rothschild ; Joel H. Spencer |
| title_fullStr | Ramsey theory Ronald L. Graham ; Bruce L. Rothschild ; Joel H. Spencer |
| title_full_unstemmed | Ramsey theory Ronald L. Graham ; Bruce L. Rothschild ; Joel H. Spencer |
| title_short | Ramsey theory |
| title_sort | ramsey theory |
| topic | Ramsey, Théorie de Ramsey, théorie de ram Combinatorial analysis Ramsey theory Ramsey-Theorie (DE-588)4212682-4 gnd |
| topic_facet | Ramsey, Théorie de Ramsey, théorie de Combinatorial analysis Ramsey theory Ramsey-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004015517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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