# Introduction to Combinatorics

John Wiley & Sons, Sep 27, 1996 - Mathematics - 195 pages
This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice.

Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material.

Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

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### Contents

 Existence 23 Sequences and Partial Orders 40 Ramsey Theory 49 Enumeration 73 Recurrence Relations and Explicit Formulas 82 Permutations and Tableaux 111
 The Polya Theory of Counting 117 Construction 135 Designs 154 Big Designs 178 Bibliography 187 Copyright

### References to this book

 Artificial Intelligence for Advanced Problem Solving TechniquesVlahavas, IoannisLimited preview - 2008
 Aspects of Combinatorics and Combinatorial Number TheorySukumar Das AdhikariLimited preview - 2002