# Combinatorics

John Wiley & Sons, Sep 24, 2003 - Mathematics - 576 pages
A mathematical gem–freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:

• Lively and engaging writing style
• Timely and appropriate examples
• Numerous well-chosen exercises
• Flexible modular format
• Optional sections and appendices

Highlights of Second Edition enhancements:

• Smoothed and polished exposition, with a sharpened focus on key ideas
• Expanded discussion of linear codes
• New optional section on algorithms
• Greatly expanded hints and answers section
• Many new exercises and examples

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### Contents

 Chapter 1 The Mathematics of Choice 1 Chapter 2 The Combinatorics of Finite Functions 117 Chapter 3 Pólyas Theory of Enumeration 175 Chapter 4 Generating Functions 253 Chapter 5 Enumeration in Graphs 337 Chapter 6 Codes and Designs 421 Appendix A1 Symmetric Polynomials 477
 Appendix A2 Sorting Algorithms 485 Appendix A3 Matrix Theory 495 Bibliography 501 Hints and Answers to Selected OddNumbered Exercises 503 Index of Notation 541 Index 547 Copyright

### Popular passages

Page xii - It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general the more difficult) the idea. Thus the idea of an "irrational" is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's.
Page 20 - It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. . . . The most important questions of life are, for the most part, really only problems of probability.

### References to this book

 Multilinear AlgebraRussell MerrisLimited preview - 1997