Introduction to Combinatorial Analysis

This introduction to combinatorial analysis defines the subject as "the number of ways there are of doing some well-defined operation."

Chapter 1 surveys that part of the theory of permutations and combinations associated with elementary algebra, which leads to the extended treatment of generating functions in Chapter 2.
Chapter 3 considers the principle of inclusion and exclusion, which is indispensable to the enumeration of permutations with restricted position given in Chapters 7 and 8.
Chapter 4 examines the enumeration of permutations in cyclic representation, while Chapter 5 surveys the theory of distributions and Chapter 6 considers partitions, compositions, and the enumeration of trees and linear graphs.
Each chapter includes a problem section.

Contents

1. Permutations and Combinations
2. Generating Functions
3. The Principle of Inclusion and Exclusion
4. The Cycles of Permutations
5. Distributions: Occupancy
6. Partitions, Compositions, Trees, and Networks
7. Permutations with Restricted Position I
8. Permutations with Restricted Position II