Aspects of Combinatorics and Combinatorial Number Theory

The author begins with a discussion of various Ramsey-type theorems in combinatorics and combinatorial number theory. He then moves on to describe many recent Ramsey-type results in combinatorics with application of topological ideas.

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The Present Volume largely concerns Ramsey-type results in combinatorial number theory. These results talk about 'unavoidable regularities'. Attempt has been made to touch upon all the classic results and, at the same time, to give glimpses of various techniques used to tackle these problems. However, most of the proofs rely on combinatorial arguments. Starting from a discussion on the pigeonhole principle (of which the classical theorem of Ramsey can be thought of a generalization) and the early results in the area of 'Ramsey-type theorems in combinatorial theory', later this book discusses the theorem of Hales and Jewett, several variations of the van der waerden's theorem, some generalizations of Schur's theorem, an introduction to Euclidean Ramsey Theory, some Ramsey-type theorems in additive number theory and application of Ramsey's theorem to number theoretic problems. Recent results on the parity of the partition function and some Ramsey-type results in partially ordered sets are also presented.