组合数学

作者简介

This third edition of Introductory Combinatorics contains extensive rewriting of some sections and the inclusion of some new material and exercises.There is enough material in this third edition for a two semester course. A first semester could have an emphasis on counting and a second semester an emphasis on graph theory.

It is difficult to assess the prerequisites for this book. Perhaps they can be best described as the mathematical maturity achieved by the successful completion of the calculus sequence and an elementary course on linear algebra. Use of calculus is minimal, and the references to linear algebra axe few and should not cause any problem to those not familiar with it.

书籍目录

Preface

Chapter 1.What is Combinatorics?

Chapter 2.The Pigeonhole Principle

Chapter 3.Permutations and Combinations

Chapter 4.Generating Permutations and Combinations

Chapter 5.The Binomial Coefficients

Chapter 6.The Inclusion-Exclusion Principle and Applications

Chapter 7.Recurrence Relations and Generating Functions

Chapter 8.Special Counting Sequences

Chapter 9.Matchings in Bipartite Graphs

Chapter 10.Combinatorial Designs

Chapter 11.Introduction to Graph Theory

Chapter 12.Digraphs and Networks

Chapter 13.More on Graph Theory

Chapter 14.Polya Counting

Answers and Hints to Exercises

Bibliography

Index

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