Polynomial Methods in Combinatorics

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Author: Larry Guth

Publisher: American Mathematical Soc.

ISBN: 1470428903

Category: Combinatorial geometry

Page: 273

View: 1784

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

A Journey Through Discrete Mathematics

A Tribute to Jiří Matoušek

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Author: Martin Loebl,Jaroslav Nešetřil,Robin Thomas

Publisher: Springer

ISBN: 3319444794

Category: Computers

Page: 810

View: 8610

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Handbook of Discrete and Computational Geometry, Third Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1351645919

Category: Computers

Page: 1928

View: 5917

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Recent Trends in Combinatorics

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Author: Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali

Publisher: Springer

ISBN: 3319242989

Category: Mathematics

Page: 778

View: 2478

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.

Graphs for Pattern Recognition

Infeasible Systems of Linear Inequalities

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Author: Damir Gainanov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110481065

Category: Mathematics

Page: 158

View: 4300

Data mining and pattern recognition are areas based on the mathematical constructions discussed in this monograph. By using combinatorial and graph theoretical techniques, it is shown how to tackle infeasible systems of linear inequalities. These are, in turn, building blocks of geometric decision rules for pattern recognition.

Surveys in Combinatorics, 1991

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Author: A. D. Keedwell,N. J. Hitchin

Publisher: Cambridge University Press

ISBN: 9780521407663

Category: Mathematics

Page: 300

View: 4367

This volume contains the invited papers presented at the British Combinatorial Conference, held at the University of Surrey in July 1991.

Frontiers In Orthogonal Polynomials And Q-series

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Author: Nashed M Zuhair,Li Xin

Publisher: World Scientific

ISBN: 981322889X

Category: Mathematics

Page: 576

View: 3229

This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10–12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate. Contents: Mourad Ismail (Richard Askey)Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton)Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series (George E Andrews)A Sturm–Liouville Theory for Hahn Difference Operator (M H Annaby, A E Hamza and S D Makharesh)Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg)Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed)A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián)The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu)Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin)Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai)From the Gaussian Circle Problem to Multivariate Shannon Sampling (Willi Freeden and M Zuhair Nashed)Weighted Partition Identities and Divisor Sums (F G Garvan)On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi)A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi)Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov)The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll)Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez)Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer)Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder)Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule)A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov)Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier)q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser)Summation Formulae for Noncommutative Hypergeometric Series (Michael J Schlosser)Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong)Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang)On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang) Readership: Graduate students and researchers interested in orthogonal polynomials and

Topics in Geometric Group Theory

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Author: Pierre de la Harpe

Publisher: University of Chicago Press

ISBN: 9780226317212

Category: Mathematics

Page: 310

View: 5337

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Combinatorial Methods in Density Estimation

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Author: Luc Devroye,Gabor Lugosi

Publisher: Springer Science & Business Media

ISBN: 9780387951171

Category: Mathematics

Page: 208

View: 2344

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

Surveys in Combinatorics 2005

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Author: Bridget S. Webb

Publisher: Cambridge University Press

ISBN: 9780521615235

Category: Mathematics

Page: 258

View: 9884

This volume provides an up-to-date overview of current research across combinatorics,.

Computer Algebra Methods for Equivariant Dynamical Systems

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Author: Karin Gatermann

Publisher: Springer

ISBN: N.A

Category: Computers

Page: 162

View: 9163

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

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Author: Christopher D. Wensley

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 6945

Surveys in Combinatorics 2013

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Author: Simon R. Blackburn,Stefanie Gerke,Mark Wildon

Publisher: Cambridge University Press

ISBN: 1107651956

Category: Computers

Page: 384

View: 1232

Surveys of recent important developments in combinatorics covering a wide range of areas in the field.

Lectures on the Ricci Flow

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Author: Peter Topping

Publisher: Cambridge University Press

ISBN: 0521689473

Category: Mathematics

Page: 113

View: 496

An introduction to Ricci flow suitable for graduate students and research mathematicians.

Algebraic, Extremal and Metric Combinatorics 1986

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Author: M. M. Deza,Philip Franklin,Michel-Marie Deza,P. Frankl,I. G. Rosenberg

Publisher: Cambridge University Press

ISBN: 9780521359238

Category: Mathematics

Page: 245

View: 3594

This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs. All the papers contain new results and many are extensive surveys of particular areas of research. Particularly valuable will be Ivanov's paper on recent Soviet research in these areas. Consequently this volume will be of great attraction to all researchers in combinatorics and to research students requiring a rapid introduction to some of the open problems in the subject.