Introduction to Combinatorial Analysis

John Riordan

Apr. 2012 · Courier Corporation

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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.