Basic Techniques of Combinatorial Theory
| Author | : Daniel I. A. Cohen |
| Publisher | : John Wiley & Sons |
| Total Pages | : 318 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : |
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Principles and Techniques in Combinatorics
| Author | : Chuan-Chong Chen |
| Publisher | : World Scientific |
| Total Pages | : 314 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9789810211394 |
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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.
Combinatorial techniques
| Author | : Sharad S. Sane |
| Publisher | : Hindustan Book Agency |
| Total Pages | : 0 |
| Release | : 2013-01-15 |
| Genre | : Mathematics |
| ISBN | : 9789380250489 |
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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.
Combinatorial Theory
| Author | : Martin Aigner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 493 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642591019 |
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This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
Combinatorics
| Author | : Peter Jephson Cameron |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 1994-10-06 |
| Genre | : Mathematics |
| ISBN | : 9780521457613 |
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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.
Combinatorial Methods
| Author | : Alexander Mikhalev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 336 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780387405629 |
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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).
Combinatorial Problems and Exercises
| Author | : L. Lovász |
| Publisher | : Elsevier |
| Total Pages | : 636 |
| Release | : 2014-06-28 |
| Genre | : Mathematics |
| ISBN | : 0080933092 |
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The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
Principles and Techniques in Combinatorics
| Author | : Chen Chuan-Chong |
| Publisher | : World Scientific |
| Total Pages | : 312 |
| Release | : 1992-07-22 |
| Genre | : Mathematics |
| ISBN | : 981436567X |
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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. Contents:Permutations and CombinationsBinomial Coefficients and Multinomial CoefficientsThe Pigeonhole Principle and Ramsey NumbersThe Principle of Inclusion and ExclusionGenerating FunctionsRecurrence Relations Readership: Undergraduates, graduates and mathematicians. keywords:Binomial Coefficients;Multinomial Coefficients;Euler Ï-Function;Enumerative Combinatorics;Addition Principle;Multiplication Principle;Combination;Permutation;Identities;Pigeon Hole Principle;Ramsey Numbers;Principle of Inclusion and Exclusion;Stirling Numbers;Derangements;Problem of Ménages;Sieve of Eratosthenes;Generating Functions;Partitions of Integers;Exponential Generating Functions;Recurrence Relations;Characteristic Polynomial;Catalan Numbers “This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses.” Mathematical Reviews
Combinatorial techniques
| Author | : Sharad S. Sane |
| Publisher | : Springer |
| Total Pages | : 477 |
| Release | : 2013-01-15 |
| Genre | : Mathematics |
| ISBN | : 938627955X |
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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.
Combinatorics and Graph Theory
| Author | : John Harris |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2009-04-03 |
| Genre | : Mathematics |
| ISBN | : 0387797114 |
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These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
