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Principles and Techniques in Combinatori - Chen Chuan-Chong

Principles and Techniques in Combinatori

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Published: 7th January 1992
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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.

"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

Preface
Notation and Abbreviation
Contents
Permutations and Combinationsp. 1
Two Basic Counting Principlesp. 1
Permutationsp. 6
Circular Permutationsp. 12
Combinationsp. 17
The Injection and Bijection Principlesp. 27
Arrangements and Selections with Repetitionsp. 32
Distribution Problemsp. 40
Binomial Coefficients and Multinomial Coefficientsp. 69
The Binomial Theoremp. 70
Combinatorial Identitiesp. 71
The Pascal's Trianglep. 76
Chu Shih-Chieh's Identityp. 78
Shortest Routes in a Rectangular Gridp. 85
Some Properties of Binomial Coefficientsp. 93
Multinomial Coefficients and the Multinomial Theoremp. 96
The Pigeonhole Principle and Ramsey Numbersp. 119
The Pigeonhole Principlep. 119
More Examplesp. 122
Ramsey Type Problems and Ramsey Numbersp. 129
Bounds for Ramsey Numbersp. 132
The Principle of Inclusion and Exclusionp. 145
The Principlep. 146
A Generalizationp. 148
Integer Solutions and Shortest Routesp. 153
Surjective Mappings and Stirling Numbers of the Second Kindp. 158
Derangements and A Generalizationp. 160
The Sieve of Eratosthenes and Euler [phi]-functionp. 163
The 'Probleme des Menages'p. 169
Generating Functionsp. 185
Ordinary Generating Functionsp. 185
Some Modelling Problemsp. 192
Partitions of Integersp. 196
Exponential Generating Functionsp. 204
Recurrence Relationsp. 225
Two Examplesp. 228
Linear Homogeneous Recurrence Relationsp. 234
General Linear Recurrence Relationsp. 241
Two Applicationsp. 244
A System of Linear Recurrence Relationsp. 251
The Method of Generating Functionsp. 256
A Nonlinear Recurrence Relation and Catalan Numbersp. 259
Oscillating Permutations and an Exponential Generating Functionp. 262
Bibliographyp. 287
Answersp. 289
Indexp. 297
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810211394
ISBN-10: 9810211392
Audience: General
Format: Paperback
Language: English
Number Of Pages: 312
Published: 7th January 1992
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 15.5 x 22.8  x 1.7
Weight (kg): 0.46