Combinatorial Methods

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Combinatorial Methods

Author : Alexander Mikhalev
Publisher : Springer Science & Business Media
ISBN 13 : 9780387405629
Total Pages : 336 pages
Book Rating : 4.4/5 (56 download)

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Book Synopsis Combinatorial Methods by : Alexander Mikhalev

Download or read book Combinatorial Methods written by Alexander Mikhalev and published by Springer Science & Business Media. This book was released on 2004 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century. This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).

Polynomial Methods in Combinatorics

Author : Larry Guth
Publisher : American Mathematical Soc.
ISBN 13 : 1470428903
Total Pages : 273 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Polynomial Methods in Combinatorics by : Larry Guth

Download or read book Polynomial Methods in Combinatorics written by Larry Guth and published by American Mathematical Soc.. This book was released on 2016-06-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorial Methods with Computer Applications

Author : Jonathan L. Gross
Publisher : CRC Press
ISBN 13 : 1584887443
Total Pages : 664 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross

Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2016-04-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Combinatorial Methods in Discrete Mathematics

Author : Vladimir N. Sachkov
Publisher : Cambridge University Press
ISBN 13 : 0521455138
Total Pages : 324 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Combinatorial Methods in Discrete Mathematics by : Vladimir N. Sachkov

Download or read book Combinatorial Methods in Discrete Mathematics written by Vladimir N. Sachkov and published by Cambridge University Press. This book was released on 1996-01-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an attempt to present some complex problems of discrete mathematics in a simple and unified form using a unique, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived.This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.

Combinatorial Methods in Density Estimation

Author : Luc Devroye
Publisher : Springer Science & Business Media
ISBN 13 : 1461301254
Total Pages : 219 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Combinatorial Methods in Density Estimation by : Luc Devroye

Download or read book Combinatorial Methods in Density Estimation written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 book is the first to explore 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.

Combinatorial Methods in Discrete Distributions

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 0471733172
Total Pages : 440 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Combinatorial Methods in Discrete Distributions by : Charalambos A. Charalambides

Download or read book Combinatorial Methods in Discrete Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.

Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization

Author : Levent Tuncel
Publisher : American Mathematical Soc.
ISBN 13 : 0821871854
Total Pages : 233 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization by : Levent Tuncel

Download or read book Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization written by Levent Tuncel and published by American Mathematical Soc.. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorial Chemistry and Technologies

Author : Stanislav Miertus
Publisher : CRC Press
ISBN 13 : 1420027840
Total Pages : 597 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Combinatorial Chemistry and Technologies by : Stanislav Miertus

Download or read book Combinatorial Chemistry and Technologies written by Stanislav Miertus and published by CRC Press. This book was released on 2005-04-12 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several books on the market cover combinatorial techniques, but they offer just a limited perspective of the field, focusing on selected aspects without examining all approaches and integrated technologies. Combinatorial Chemistry and Technologies: Methods and Applications answers the demand for a complete overview of the field, covering all of the

Introduction to Combinatorial Testing

Author : D. Richard Kuhn
Publisher : CRC Press
ISBN 13 : 1466552301
Total Pages : 341 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Introduction to Combinatorial Testing by : D. Richard Kuhn

Download or read book Introduction to Combinatorial Testing written by D. Richard Kuhn and published by CRC Press. This book was released on 2016-04-19 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial testing of software analyzes interactions among variables using a very small number of tests. This advanced approach has demonstrated success in providing strong, low-cost testing in real-world situations. Introduction to Combinatorial Testing presents a complete self-contained tutorial on advanced combinatorial testing methods for real-world software. The book introduces key concepts and procedures of combinatorial testing, explains how to use software tools for generating combinatorial tests, and shows how this approach can be integrated with existing practice. Detailed explanations and examples clarify how and why to use various techniques. Sections on cost and practical considerations describe tradeoffs and limitations that may impact resources or funding. While the authors introduce some of the theory and mathematics of combinatorial methods, readers can use the methods without in-depth knowledge of the underlying mathematics. Accessible to undergraduate students and researchers in computer science and engineering, this book illustrates the practical application of combinatorial methods in software testing. Giving pointers to freely available tools and offering resources on a supplementary website, the book encourages readers to apply these methods in their own testing projects.

Global Methods for Combinatorial Isoperimetric Problems

Author : L. H. Harper
Publisher :
ISBN 13 : 0511189745
Total Pages : 248 pages
Book Rating : 4.5/5 (111 download)

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Book Synopsis Global Methods for Combinatorial Isoperimetric Problems by : L. H. Harper

Download or read book Global Methods for Combinatorial Isoperimetric Problems written by L. H. Harper and published by . This book was released on 2006-05-16 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores global methods in combinatorial optimization and is suitable for graduate students and researchers.

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Author : Mauro Di Nasso
Publisher : Springer
ISBN 13 : 3030179567
Total Pages : 206 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso

Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Polynomial Identities And Combinatorial Methods

Author : Antonio Giambruno
Publisher : CRC Press
ISBN 13 : 9780203911549
Total Pages : 442 pages
Book Rating : 4.9/5 (115 download)

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Book Synopsis Polynomial Identities And Combinatorial Methods by : Antonio Giambruno

Download or read book Polynomial Identities And Combinatorial Methods written by Antonio Giambruno and published by CRC Press. This book was released on 2003-05-20 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.

Combinatorial Methods

Author : Vladimir Shpilrain
Publisher : Springer Science & Business Media
ISBN 13 : 038721724X
Total Pages : 322 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Combinatorial Methods by : Vladimir Shpilrain

Download or read book Combinatorial Methods written by Vladimir Shpilrain and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

Combinatorial Methods

Author : Jerome K. Percus
Publisher : Springer Science & Business Media
ISBN 13 : 1461264049
Total Pages : 203 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Combinatorial Methods by : Jerome K. Percus

Download or read book Combinatorial Methods written by Jerome K. Percus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not a large overstatement to claim that mathematics has traditionally arisen from attempts to understand quite concrete events in the physical world. The accelerated sophistication of the mathematical community has perhaps obscured this fact, especially during the present century, with the abstract becoming the hallmark of much of respectable mathematics. As a result of the inaccessibility of such work, practicing scientists have often been compelled to fashion their own mathematical tools, blissfully unaware of their prior existence in far too elegant and far too general form. But the mathematical sophistication of scientists has grown rapidly too, as has the scientific sophistication of many mathematicians, and the real worl- suitably defined - is once more serving its traditional role. One of the fields most enriched by this infusion has been that of combinatorics. This book has been written in a way as a tribute to those natural scientists whose breadth of vision has inparted a new vitality to a dormant giant. The present text arose out of a course in Combinatorial Methods given by the writer at the Courant Institute during 1967-68. Its structure has been determined by an attempt to reach an informed but heterogeneous group of students in mathematics, physics, and chemistry. Its lucidity has been enhanced immeasurably by the need to satisfy a very resolute critic, Professor Ora E. Percus, who is responsible for the original lecture notes as well as for their major modifications.

Algebraic and Combinatorial Methods in Operations Research

Author : R.E. Burkard
Publisher : Elsevier
ISBN 13 : 9780080872063
Total Pages : 380 pages
Book Rating : 4.8/5 (72 download)

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Book Synopsis Algebraic and Combinatorial Methods in Operations Research by : R.E. Burkard

Download or read book Algebraic and Combinatorial Methods in Operations Research written by R.E. Burkard and published by Elsevier. This book was released on 1984-01-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time, this book unites different algebraic approaches for discrete optimization and operations research. The presentation of some fundamental directions of this new fast developing area shows the wide range of its applicability. Specifically, the book contains contributions in the following fields: semigroup and semiring theory applied to combinatorial and integer programming, network flow theory in ordered algebraic structures, extremal optimization problems, decomposition principles for discrete structures, Boolean methods in graph theory and applications.

Combinatorial Methods with Computer Applications

Author : Jonathan L. Gross
Publisher : CRC Press
ISBN 13 : 1584887435
Total Pages : 664 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross

Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2007-11-16 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Combinatorial Methods and Models

Author : Rudolf Ahlswede
Publisher : Springer
ISBN 13 : 3319531395
Total Pages : 385 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Combinatorial Methods and Models by : Rudolf Ahlswede

Download or read book Combinatorial Methods and Models written by Rudolf Ahlswede and published by Springer. This book was released on 2017-06-30 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.