Aspects of Combinatorics and Combinatorial Number Theory

Sukumar Das Adhikari

156 pages, parution le 09/01/2002

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Résumé

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 classical 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 number 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.

Preliminary knowledge of elementary number theory, linear algebra, the rudiments of point-set topology and some basic results in the theory of finite fields are the prerequisites for this book.

Contents

Preface

Notations and terminologies

Chapter 1 : Classical Ramsey-type theorems
Chapter 2 : van des Waerden revisited
Chapter 3 : Generalizations of Schur's theorem
Chapter 4 : Topological methods
Chapter 5 : Euclidean Ramsey theory
Chapter 6 : Additive number Theory and related questions
Chapter 7 : Partitions of integers
Chapter 8 : Ramsey-type results in posets
Chapter 9 : Solutions to selected exercises

Bibliography

Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Alpha
Auteur(s)	Sukumar Das Adhikari
Parution	09/01/2002
Nb. de pages	156
Format	16 x 24,5
Couverture	Broché
Poids	522g
Intérieur	Noir et Blanc
EAN13	9781842650493
ISBN13	978-1-84265-049-3