Introduction to Combinatorial Analysis (Dover Books on Mathematics)

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. 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. 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. Cover; Title Page; Copyright Page; Dedication; Preface; 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; Index