Combinatorial Number Theory and Additive Group Theory

• Main Authors: Geroldinger, Alfred (Author), Ruzsa, Imre Z. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Series: Advanced Courses in Mathematics - CRM Barcelona, Centre de Recerca Matemàtica
• Subjects: Mathematics.; Discrete mathematics.; Combinatorics.; Discrete Mathematics.

This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics. The first two parts, which form the bulk of the volume, contain the two main advanced courses, Additive Group Theory and Non-Unique F...

Table of Contents:

• Additive Group Theory and Non-unique Factorizations
• Notation
• Basic concepts of non-unique factorizations
• The Davenport constant and first precise arithmetical results
• The structure of sets of lengths
• Addition theorems and direct zero-sum problems
• Inverse zero-sum problems and arithmetical consequences
• Sumsets and Structure
• Notation
• Cardinality inequalities
• Structure of sets with few sums
• Location and sumsets
• Density
• Measure and topology
• Exercises
• Thematic seminars
• A survey on additive and multiplicative decompositions of sumsets and of shifted sets
• On the detailed structure of sets with small additive property
• The isoperimetric method
• Additive structure of difference sets
• The polynomial method in additive combinatorics
• Problems in additive number theory, III
• Incidences and the spectra of graphs
• Multi-dimensional inverse additive problems.