Principles and Techniques in Combinatorics

Principles and Techniques in Combinatorics

by Koh Khee-Meng
     
 

Product Details

ISBN-13:
9789810211394
Publisher:
World Scientific Publishing Co Pte Ltd
Publication date:
07/28/1992
Edition description:
New Edition
Pages:
312
Sales rank:
446,024
Product dimensions:
6.00(w) x 9.00(h) x 0.65(d)

Table of Contents

Preface
Notation and Abbreviation
Contents
1Permutations and Combinations1
1.1Two Basic Counting Principles1
1.2Permutations6
1.3Circular Permutations12
1.4Combinations17
1.5The Injection and Bijection Principles27
1.6Arrangements and Selections with Repetitions32
1.7Distribution Problems40
2Binomial Coefficients and Multinomial Coefficients69
2.2The Binomial Theorem70
2.3Combinatorial Identities71
2.4The Pascal's Triangle76
2.5Chu Shih-Chieh's Identity78
2.6Shortest Routes in a Rectangular Grid85
2.7Some Properties of Binomial Coefficients93
2.8Multinomial Coefficients and the Multinomial Theorem96
3The Pigeonhole Principle and Ramsey Numbers119
3.2The Pigeonhole Principle119
3.3More Examples122
3.4Ramsey Type Problems and Ramsey Numbers129
3.5Bounds for Ramsey Numbers132
4The Principle of Inclusion and Exclusion145
4.2The Principle146
4.3A Generalization148
4.4Integer Solutions and Shortest Routes153
4.5Surjective Mappings and Stirling Numbers of the Second Kind158
4.6Derangements and A Generalization160
4.7The Sieve of Eratosthenes and Euler [phi]-function163
4.8The 'Probleme des Menages'169
5Generating Functions185
5.1Ordinary Generating Functions185
5.2Some Modelling Problems192
5.3Partitions of Integers196
5.4Exponential Generating Functions204
6Recurrence Relations225
6.2Two Examples228
6.3Linear Homogeneous Recurrence Relations234
6.4General Linear Recurrence Relations241
6.5Two Applications244
6.6A System of Linear Recurrence Relations251
6.7The Method of Generating Functions256
6.8A Nonlinear Recurrence Relation and Catalan Numbers259
6.9Oscillating Permutations and an Exponential Generating Function262
Bibliography287
Answers289
Index297

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