Aspects Of Combinatorics And Combinatorial Number Theory
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Combinatorial Number Theory and Additive Group Theory
Author: Alfred Geroldinger
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-15
Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.
Aspects of Combinatorics and Combinatorial Number Theory
Author: Sukumar Das Adhikari
language: en
Publisher: Alpha Science International Limited
Release Date: 2002
The author discusses various Ramsey-type theorems in combinatorics and combinatorial number theory. While many of the main results are classic, recent progress and further open questions are described to motivate researchers. In classical theorems, wherever possible, proofs are kept different from those in Graham, Rothschild and Spencer's book. For instance, Johnson's proof has been given for Erdoes-Szekeres Theorem, mentioning references to other proofs. For Hilbert's theorem, after giving the dynamical proof following Furstenburg, a sketch of Hilbert's original proof is also given. The last part of the book describes many rather recent Ramsey-type results in combinatorics with application of topological ideas. It does not touch much of the graph theoretic part of the theory.
Combinatorial and Additive Number Theory III
Author: Melvyn B. Nathanson
language: en
Publisher: Springer Nature
Release Date: 2019-12-10
Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.