Combinatorial Techniques

Author : Sharad S. Sane
Publisher : Hindustan Book Agency
Page : 0 pages
File Size : 51,6 Mb
Release : 2013-01-15
Category : Mathematics
ISBN : 9380250487

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Combinatorial techniques by Sharad S. Sane Pdf

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.

Author : Sharad S. Sane
Publisher : Springer
Page : 477 pages
File Size : 50,8 Mb
Release : 2013-01-15
Category : Mathematics
ISBN : 9789386279552

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Combinatorial techniques by Sharad S. Sane Pdf

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.

Author : Peter Jephson Cameron
Publisher : Cambridge University Press
Page : 372 pages
File Size : 49,6 Mb
Release : 1994-10-06
Category : Mathematics
ISBN : 0521457610

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Combinatorics by Peter Jephson Cameron Pdf

Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.

Author : Chuan-Chong Chen,Khee Meng Koh,Koh Khee-Meng
Publisher : World Scientific
Page : 314 pages
File Size : 41,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9810211392

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Principles and Techniques in Combinatorics by Chuan-Chong Chen,Khee Meng Koh,Koh Khee-Meng Pdf

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Author : Daniel I. A. Cohen
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 47,9 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015016365325

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Basic Techniques of Combinatorial Theory by Daniel I. A. Cohen Pdf

Author : Alexander Mikhalev,Vladimir Shpilrain,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 49,8 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 : Klaus Jansen
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 49,5 Mb
Release : 2004-08-11
Category : Computers
ISBN : 9783540228943

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Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques by Klaus Jansen Pdf

This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, error-correcting codes, and other applications of approximation and randomness.

Author : Vladimir N. Sachkov
Publisher : Cambridge University Press
Page : 324 pages
File Size : 54,5 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 : Radislav A. Potyrailo,Vladimir M. Mirsky
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 40,6 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 : Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 50,5 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 : Luc Devroye,Gabor Lugosi
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 46,6 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 : Jerome K. Percus
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 44,6 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 : 51,8 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 : N. Balakrishnan
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 49,6 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 : 333 pages
File Size : 42,7 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 re