Additive Combinatorics

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Additive Combinatorics

Terence Tao,Van H. Vu
Additive Combinatorics Book PDF

Author : Terence Tao,Van H. Vu
Publisher : Cambridge University Press
Page : 18 pages
File Size : 52,7 Mb
Release : 2006-09-14
Category : Mathematics
ISBN : 9781139458344

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Additive Combinatorics by Terence Tao,Van H. Vu Pdf

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Additive Combinatorics

Andrew Granville,Melvyn Bernard Nathanson,Jozsef Solymosi
Additive Combinatorics Book PDF

Author : Andrew Granville,Melvyn Bernard Nathanson,Jozsef Solymosi
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 55,8 Mb
Release : 2024-06-16
Category : Mathematics
ISBN : 0821870394

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Additive Combinatorics by Andrew Granville,Melvyn Bernard Nathanson,Jozsef Solymosi Pdf

This book, based in part on lectures delivered at the 2006 CRM-Clay School on Additive Combinatorics, brings together some of the top researchers in one of the hottest topics in analysis today. This new subject brings together ideas from many different areas to prove some extraordinary results. The book encompasses proceedings from the school, articles on open questions in additive combinatorics, and new research.

Additive Combinatorics

Bela Bajnok
Additive Combinatorics Book PDF

Author : Bela Bajnok
Publisher : CRC Press
Page : 390 pages
File Size : 48,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781351137614

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Additive Combinatorics by Bela Bajnok Pdf

Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers

Graph Theory and Additive Combinatorics

Yufei Zhao
Graph Theory and Additive Combinatorics Book PDF

Author : Yufei Zhao
Publisher : Cambridge University Press
Page : 336 pages
File Size : 41,7 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.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 46,5 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.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 55,9 Mb
Release : 2009-06-04
Category : Mathematics
ISBN : 9783764389628

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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.

Combinatorial and Additive Number Theory IV

Melvyn B. Nathanson
Combinatorial and Additive Number Theory IV Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 445 pages
File Size : 46,7 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.

Combinatorial and Additive Number Theory

Melvyn B. Nathanson
Combinatorial and Additive Number Theory Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer
Page : 312 pages
File Size : 45,5 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.

Combinatorial and Additive Number Theory III

Melvyn B. Nathanson
Combinatorial and Additive Number Theory III Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 237 pages
File Size : 48,7 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.

Combinatorics and Finite Geometry

Steven T. Dougherty
Combinatorics and Finite Geometry Book PDF

Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 41,6 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030563950

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Combinatorics and Finite Geometry by Steven T. Dougherty Pdf

This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Recent Trends in Combinatorics

Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali
Recent Trends in Combinatorics Book PDF

Author : Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali
Publisher : Springer
Page : 778 pages
File Size : 44,6 Mb
Release : 2016-04-12
Category : Mathematics
ISBN : 9783319242989

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Recent Trends in Combinatorics by Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali Pdf

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

Analytic Combinatorics

Philippe Flajolet,Robert Sedgewick
Analytic Combinatorics Book PDF

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 52,6 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Number Theory and Related Fields

Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Number Theory and Related Fields Book PDF

Author : Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 50,8 Mb
Release : 2013-05-16
Category : Mathematics
ISBN : 9781461466420

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Number Theory and Related Fields by Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin Pdf

“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​

Additive Combinatorics

Andrew Granville
Additive Combinatorics Book PDF

Author : Andrew Granville
Publisher : American Mathematical Soc.
Page : 335 pages
File Size : 53,8 Mb
Release : 2007
Category : Mathematics
ISBN : 0821843516

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Additive Combinatorics by Andrew Granville Pdf

One of the most active areas in mathematics today is the rapidly emerging new topic of ``additive combinatorics''. Building on Gowers' use of the Freiman-Ruzsa theorem in harmonic analysis (in particular, his proof of Szemeredi's theorem), Green and Tao famously proved that there are arbitrarily long arithmetic progressions of primes, and Bourgain and his co-authors have given non-trivial estimates for hitherto untouchably short exponential sums. There are further important consequences in group theory and in complexity theory and compelling questions in ergodic theory, discrete geometry and many other disciplines. The basis of the subject is not too difficult: it can be best described as the theory of adding together sets of numbers; in particular, understanding the structure of the two original sets if their sum is small. This book brings together key researchers from all of these different areas, sharing their insights in articles meant to inspire mathematicians coming from all sorts of different backgrounds.

Surveys in Combinatorics 2024

Felix Fischer,Robert Johnson
Surveys in Combinatorics 2024 Book PDF

Author : Felix Fischer,Robert Johnson
Publisher : Cambridge University Press
Page : 305 pages
File Size : 46,5 Mb
Release : 2024-06-13
Category : Mathematics
ISBN : 9781009490535

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Surveys in Combinatorics 2024 by Felix Fischer,Robert Johnson Pdf

This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.