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.

Introduction to Combinatorial Analysis (Dover Books on Mathematics)

Science & Math

John Riordan

Mathematics

Dover Publications

COMBINATORIAL IDENTITIES explores the possibility of finding areas of order and coherence in combinatorial identitiesâ€”identities between, or in terms of, combinatorial entitiesâ€”within mathematical settings. Because this is a naturally chaotic subject, several divergent but related topics appear in the discussion. The most important of these is the use of inverse relations. COMBINATORIAL IDENTITIES features the most extensive array of inverse relations available, and the known uses of these in probability and statistics suggest wider uses elsewhere. The book also includes a survey of number-theoretical aspects of partition polynomials. Identities have long been a subject of interest in mathematics. This new study invokes a reinvigoration of the older aspects of mathematics, supplying it with a fresh outlook. Large problem sections illustrate and expand the development of the material presented.

Combinatorial identities

R.E. Krieger Pub. Co.

An Introduction to Combinatorial Analysis

Princeton University Press

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Books by John Riordan