Additive Number Theory

Inverse Problems and the Geometry of Sumsets

By: Melvyn B. Nathanson

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Hardcover | 22 August 1996

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316 Pages

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24.13 x 15.88 x 1.91

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Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

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Preface
Notation
Simple inverse theorems	p. 1
Sums of congruence classes	p. 41
Sums of distinct congruence classes	p. 77
Kneser's theorem for groups	p. 109
Sums of vectors in Euclidean space	p. 133
Geometry of numbers	p. 167
Plunnecke's inequality	p. 201
Freiman's theorem	p. 231
Applications of Freiman's theorem	p. 255
References	p. 283
Index	p. 292
Table of Contents provided by Blackwell. All Rights Reserved.

Additive Number Theory

Inverse Problems and the Geometry of Sumsets

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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