Introduction to Combinatorial Analysis

<p>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 that finds a place in books on elementary algebra which leads to the extended treatment of generation functions in Chapter 2 where an important result is the introduction of a set of multivariable polynomials.<br>Chapter 3 contains an extended treatment of 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 and Chapter 5 surveys the theory of distributions. Chapter 6 considers partitions compositions and the enumeration of trees and linear graphs.<br>Each chapter includes a lengthy problem section intended to develop the text and to aid the reader. These problems assume a certain amount of mathematical maturity. Equations theorems sections examples and problems are numbered consecutively in each chapter and are referred to by these numbers in other chapters.</p>