Additive Number Theory: Inverse Problems and the Geometry of Sumsets / Edition 1

by Melvyn B. Nathanson

Overview

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, Plünnecke, 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.

Product Details

ISBN-13:	9780387946559
Publisher:	Springer New York
Publication date:	08/22/1996
Series:	Graduate Texts in Mathematics , #165
Edition description:	1996
Pages:	295
Product dimensions:	6.14(w) x 9.21(h) x 0.03(d)