Principles and Techniques in Combinatorics

By: Chuan Chong Chen, Khee-meng Koh

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Hardcover | 1 December 1991

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312 Pages

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22.86 x 15.24 x 1.91

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“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.”

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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.

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Preface
Notation and Abbreviation
Contents
Permutations and Combinations	p. 1
Two Basic Counting Principles	p. 1
Permutations	p. 6
Circular Permutations	p. 12
Combinations	p. 17
The Injection and Bijection Principles	p. 27
Arrangements and Selections with Repetitions	p. 32
Distribution Problems	p. 40
Binomial Coefficients and Multinomial Coefficients	p. 69
The Binomial Theorem	p. 70
Combinatorial Identities	p. 71
The Pascal's Triangle	p. 76
Chu Shih-Chieh's Identity	p. 78
Shortest Routes in a Rectangular Grid	p. 85
Some Properties of Binomial Coefficients	p. 93
Multinomial Coefficients and the Multinomial Theorem	p. 96
The Pigeonhole Principle and Ramsey Numbers	p. 119
The Pigeonhole Principle	p. 119
More Examples	p. 122
Ramsey Type Problems and Ramsey Numbers	p. 129
Bounds for Ramsey Numbers	p. 132
The Principle of Inclusion and Exclusion	p. 145
The Principle	p. 146
A Generalization	p. 148
Integer Solutions and Shortest Routes	p. 153
Surjective Mappings and Stirling Numbers of the Second Kind	p. 158
Derangements and A Generalization	p. 160
The Sieve of Eratosthenes and Euler [phi]-function	p. 163
The 'Probleme des Menages'	p. 169
Generating Functions	p. 185
Ordinary Generating Functions	p. 185
Some Modelling Problems	p. 192
Partitions of Integers	p. 196
Exponential Generating Functions	p. 204
Recurrence Relations	p. 225
Two Examples	p. 228
Linear Homogeneous Recurrence Relations	p. 234
General Linear Recurrence Relations	p. 241
Two Applications	p. 244
A System of Linear Recurrence Relations	p. 251
The Method of Generating Functions	p. 256
A Nonlinear Recurrence Relation and Catalan Numbers	p. 259
Oscillating Permutations and an Exponential Generating Function	p. 262
Bibliography	p. 287
Answers	p. 289
Index	p. 297
Table of Contents provided by Blackwell. All Rights Reserved.

Principles and Techniques in Combinatorics

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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