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Additive Number Theory: Additive Number Theory: Inverse Problems and the Geometry of Sumsets

English · Hardback

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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, 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

Authors M. B. Nathanson, Melvyn B. Nathanson, Melvyn B Nathanson
Publisher Springer, Berlin
 
Content Book
Product form Hardback
Publication date 01.01.1960
Subject Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematica
Social sciences, law, business > Business > Business administration
 
EAN 9780387946559
ISBN 978-0-387-94655-9
Pages 295
Illustrations XIV, 295 p.
Dimensions (packing) 15.7 x 24.3 x 2.3 cm
Weight (packing) 608 g
 
Set Additive Number Theory
Additive Number Theory
Series Graduate Texts in Mathematics > Vol.165
Graduate Texts in Mathematics > 165
Subjects Zahlentheorie
Geometrie
Raumlehre
CON_D035
 

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