Combinatorial Methods

Author : Alexander Mikhalev,Vladimir Shpilrain,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 43,7 Mb
Release : 2004
Category : Mathematics
ISBN : 0387405623

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Combinatorial Methods by Alexander Mikhalev,Vladimir Shpilrain,Jie-tai Yu Pdf

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).

Author : Luc Devroye,Gabor Lugosi
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301257

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Combinatorial Methods in Density Estimation by Luc Devroye,Gabor Lugosi Pdf

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.

Author : Jonathan L. Gross
Publisher : CRC Press
Page : 664 pages
File Size : 52,5 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781584887447

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Combinatorial Methods with Computer Applications by Jonathan L. Gross Pdf

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

Author : Vladimir N. Sachkov
Publisher : Cambridge University Press
Page : 324 pages
File Size : 55,5 Mb
Release : 1996-01-11
Category : Mathematics
ISBN : 9780521455138

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Combinatorial Methods in Discrete Mathematics by Vladimir N. Sachkov Pdf

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.

Author : Larry Guth
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 50,5 Mb
Release : 2016-06-10
Category : Combinatorial analysis
ISBN : 9781470428907

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Polynomial Methods in Combinatorics by Larry Guth Pdf

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.

Author : Levent Tuncel
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 50,6 Mb
Release : 2024-06-13
Category : Mathematics
ISBN : 9780821871850

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Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization by Levent Tuncel Pdf

Author : Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 40,5 Mb
Release : 2012-11-12
Category : Mathematics
ISBN : 9780387217246

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Combinatorial Methods by Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu Pdf

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.

Author : Mauro Di Nasso,Isaac Goldbring,Martino Lupini
Publisher : Springer
Page : 206 pages
File Size : 49,9 Mb
Release : 2019-05-23
Category : Mathematics
ISBN : 9783030179564

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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by Mauro Di Nasso,Isaac Goldbring,Martino Lupini Pdf

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.

Author : Jerome K. Percus
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461264040

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Combinatorial Methods by Jerome K. Percus Pdf

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.

Author : Jonathan L. Gross
Publisher : CRC Press
Page : 664 pages
File Size : 52,7 Mb
Release : 2007-11-16
Category : Mathematics
ISBN : 9781584887430

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Combinatorial Methods with Computer Applications by Jonathan L. Gross Pdf

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.

Author : Radislav A. Potyrailo,Vladimir M. Mirsky
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 44,9 Mb
Release : 2009-03-21
Category : Science
ISBN : 9780387737133

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Combinatorial Methods for Chemical and Biological Sensors by Radislav A. Potyrailo,Vladimir M. Mirsky Pdf

Chemical sensors are in high demand for applications as varied as water pollution detection, medical diagnostics, and battlefield air analysis. Designing the next generation of sensors requires an interdisciplinary approach. The book provides a critical analysis of new opportunities in sensor materials research that have been opened up with the use of combinatorial and high-throughput technologies, with emphasis on experimental techniques. For a view of component selection with a more computational perspective, readers may refer to the complementary volume of Integrated Analytical Systems edited by M. Ryan et al., entitled “Computational Methods for Sensor Material Selection”.

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
Page : 440 pages
File Size : 48,9 Mb
Release : 2005-06-24
Category : Mathematics
ISBN : 9780471733171

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Combinatorial Methods in Discrete Distributions by Charalambos A. Charalambides Pdf

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.

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241409

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Advances in Combinatorial Methods and Applications to Probability and Statistics by N. Balakrishnan Pdf

Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.

Author : D. Richard Kuhn,Raghu N. Kacker,Yu Lei
Publisher : CRC Press
Page : 341 pages
File Size : 43,6 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781466552302

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Introduction to Combinatorial Testing by D. Richard Kuhn,Raghu N. Kacker,Yu Lei Pdf

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.

Author : L. H. Harper
Publisher : Unknown
Page : 248 pages
File Size : 42,8 Mb
Release : 2006-05-16
Category : Mathematics
ISBN : 9780511189746

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Global Methods for Combinatorial Isoperimetric Problems by L. H. Harper Pdf

This text explores global methods in combinatorial optimization and is suitable for graduate students and researchers.