Principles and Techniques in Combinatorics
by Chuan-Chong, Chen; Khee-Meng, KohFormat: Paperback
Pub. Date: 1992-09-01
Publisher(s): World Scientific Pub Co Inc
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Summary
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.
Table of Contents
| 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. |
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