Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Graduate Texts in Mathematics, 165, Band 165).

Nathanson, Melvyn B.;

ISBN 10: 0387946551 / ISBN 13: 9780387946559

Published by New York. Springer-Verlag., 1996

About this Item

Zust: Gutes Exemplar. 293 Seiten, mit Abbildungen, Englisch 598g.

Seller Inventory # 494621

Bibliographic Details

• Title: Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Graduate Texts in Mathematics, 165, Band 165).
• Publisher: New York. Springer-Verlag.
• Publication Date: 1996
• Language: English
• ISBN 10: 0387946551
• ISBN 13: 9780387946559
• Binding: Karton
• Condition: Sehr gut
• Seller catalogs:
  • Mathematik

About this title

Synopsis

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.

From the Back Cover

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(actual symbol not reproducible)2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In 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 remarkable 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, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza 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. Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and self-contained account of this subject. In particular, it contains complete proofs of results from exterior algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis.