Introduction to Combinatorial Analysis

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Courier Corporation, 13 déc. 2002 - 256 pages

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.

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John Riordan. An Introduction to Combinatorial Analysis John Riordan DOVER PUBLICATIONS , INC . Mineola , New York Bibliographical Note This Dover edition , first published in 2002.
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John Riordan. Bibliographical Note This Dover edition , first published in 2002 , is an unabridged republication of the work first published by John Wiley & Sons , Inc. , New York , in 1958. The errata list was added in a later printing ...
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Expressions et termes fréquents

a₁ appear Bell polynomial binomial coefficients binomial moments C₁ cards Chapter coefficients column combinatorial corresponding cycle index cycle indicator cycle of length decks defined denoting a derivative Derive the recurrence different cells distinct distribution Dn(t E. T. Bell elements enumerator by number equation equivalent Example exp r(x expansion exponential generating function factor factorial moments follows at once given Hence hit polynomial k₁ labeled Latin rectangles linear graphs lines mathematical induction ménage ménage problem networks Note noticed number of partitions number of permutations number of points objects of specification odd permutations ordinary generating function P₁ prime denoting r-combinations r-permutations recurrence relation rook polynomial rooted trees sequence Stirling numbers symmetric functions t₁ Theorem things total number Un(t variables verify the table Write X X X X X

Informations bibliographiques

TitreIntroduction to Combinatorial Analysis
Dover Books on Mathematics
AuteurJohn Riordan
Éditionillustrée, réimprimée
ÉditeurCourier Corporation, 2002
ISBN0486425363, 9780486425368
Longueur256 pages
  
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