Combinatorial Number Theory And Additive Group Theory

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 52,8 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9783764389611

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

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.

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 445 pages
File Size : 44,6 Mb
Release : 2021-08-12
Category : Mathematics
ISBN : 9783030679965

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Combinatorial and Additive Number Theory IV by Melvyn B. Nathanson Pdf

This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop 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, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Author : Melvyn B. Nathanson
Publisher : Springer
Page : 309 pages
File Size : 46,5 Mb
Release : 2014-10-18
Category : Mathematics
ISBN : 9781493916016

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Combinatorial and Additive Number Theory by Melvyn B. Nathanson Pdf

This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.

Author : David J. Grynkiewicz
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 42,7 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9783319004167

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Structural Additive Theory by David J. Grynkiewicz Pdf

​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Author : Bruce Landman,Melvyn B. Nathanson,Jaroslav Nešetril,Richard J. Nowakowski,Carl Pomerance,Aaron Robertson
Publisher : Walter de Gruyter
Page : 168 pages
File Size : 51,5 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9783110280616

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Combinatorial Number Theory by Bruce Landman,Melvyn B. Nathanson,Jaroslav Nešetril,Richard J. Nowakowski,Carl Pomerance,Aaron Robertson Pdf

This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.

Author : Paul Erdős,Ronald L. Graham
Publisher : Unknown
Page : 134 pages
File Size : 47,6 Mb
Release : 1980
Category : Combinatorial analysis
ISBN : STANFORD:36105032602836

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Old and New Problems and Results in Combinatorial Number Theory by Paul Erdős,Ronald L. Graham Pdf

Author : Gilbert Baumslag,Charles F. III Miller
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397304

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Algorithms and Classification in Combinatorial Group Theory by Gilbert Baumslag,Charles F. III Miller Pdf

The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 2020
Category : Combinatorial number theory
ISBN : 3030311074

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Combinatorial and Additive Number Theory III by Anonim Pdf

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.

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 237 pages
File Size : 52,6 Mb
Release : 2019-12-10
Category : Mathematics
ISBN : 9783030311063

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Combinatorial and Additive Number Theory III by Melvyn B. Nathanson Pdf

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.

Author : Melvyn B. Nathanson
Publisher : Springer
Page : 310 pages
File Size : 40,8 Mb
Release : 2018-01-13
Category : Mathematics
ISBN : 9783319680323

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Combinatorial and Additive Number Theory II by Melvyn B. Nathanson Pdf

Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 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. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.

Author : B. Chandler,W. Magnus
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394877

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The History of Combinatorial Group Theory by B. Chandler,W. Magnus Pdf

One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.

Author : David Chudnovsky,Gregory Chudnovsky
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 50,9 Mb
Release : 2010-08-26
Category : Mathematics
ISBN : 9780387683614

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Additive Number Theory by David Chudnovsky,Gregory Chudnovsky Pdf

This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.

Author : Roger C. Lyndon,Paul E. Schupp
Publisher : Springer
Page : 354 pages
File Size : 40,6 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783642618963

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Combinatorial Group Theory by Roger C. Lyndon,Paul E. Schupp Pdf

From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews

Author : Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 45,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828229

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Combinatorial and Geometric Group Theory by Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain Pdf

This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Author : Yufei Zhao
Publisher : Cambridge University Press
Page : 336 pages
File Size : 50,7 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781009310932

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Graph Theory and Additive Combinatorics by Yufei Zhao Pdf

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.