Aspects of Combinatorics and Combinatorial Number Theory

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CRC Press, 2002 - 156 Seiten
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Aspects of Combinatorics and Combinatorial Number Theory discusses various Ramsey-type theorems in combinatorics and combinatorial number theory. While many of the main results are classic, the book describes recent progress and considers unsolved questions in the field. For classical theorems, whenever possible, the author presents different proofs than those offered in Graham, Rothschild, and Spencer's book. For instance, Johnson's proof has been given for Erdoes-Szekeres Theorem, and in establishing that proof, the author makes reference to the other proofs. The first part of the book is primarily concerned with the history, context, and rudiments of the subject, and it requires only a basic maturity in mathematical thinking. The later parts and the remarks following each section describe many rather recent Ramsey-type results in combinatorics with application of topological ideas. These parts require some training in algebra and topology.
 

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Inhalt

Preface vii
1
van der Waerden revisited
23
Generalizations of Schurs theorem
37
Topological methods
49
Euclidean Ramsey theory
61
Additive number Theory and related questions
75
Partitions of integers
95
Ramseytype results in posets
117
Solutions to selected exercises
129
Bibliography
143
Index
153
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Ordered Sets
Egbert Harzheim
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