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Generatingfunctionology.

By: Wilf, Herbert S.
Material type: TextTextSeries: eBooks on Demand.Publisher: Burlington : Elsevier Science, 2014Description: 1 online resource (193 p.).ISBN: 9781483276632.Subject(s): Generating functionsGenre/Form: Electronic books.Additional physical formats: Print version:: GeneratingfunctionologyDDC classification: 515 LOC classification: QA353.G44 W55 2014Online resources: Click here to view this ebook.
Contents:
Front Cover; Generatingfunctionology; Copyright Page; Preface; Table of Contents; Chapter 1. Introductory Ideas and Examples; 1.1 An easy two term recurrence; 1.2 A slightly harder two term recurrence; 1.3 A three term recurrence; 1.4 A three term boundary valueproblem; 1.5 Two independent variables; 1.6 Another 2-variable case; Exercises; Chapter 2. Series; 2.1 Formal power series; 2.2 The calculus of formal ordinary power seriesgenerating functions; 2.3 The calculus of formal exponential generating functions; 2.4 Power series, analytic theory; 2.5 Some useful power series
2.6 Dirichlet series, formal theoryExercises; Chapter 3. Cards, Decks, and Hands:The Exponential Formula; 3.1 Introduction; 3.2 Definitions and a question; 3.3 Examples of exponential families; 3.4 The main counting theorems; 3.5 Permutations and their cycles; 3.6 Set partitions; 3.7 A subclass of permutations; 3.8 Involutions, etc; 3.9 2-regular Graphs; 3.10 Counting connected graphs; 3.11 Counting labeled bipartite graphs; 3.12 Counting labeled trees; 3.13 Exponential families and polynomials of'binomial type.'; 3.14 Unlabeled cards and hands; 3.15 The money changing problem
3.16 Partitions of integers3.17 Rooted trees and forests; 3.18 Historical notes; Exercises; Chapter 4. Applications of Generating Functions; 4.1 Generating functions find averages, etc; 4.2 A generatingfunctionological view of the sieve method; 4.3 The 'Snake Oil' method for easier combinatorial identities; 4.4 WZ pairs prove harder identities; 4.5 Generating functions and unimodality, convexity, etc; 4.6 Generating functions prove congruences; Exercises; Chapter 5. Analytic and Asymptotic Methods; 5.1 The Lagrange Inversion Formula; 5.2 Analyticity and asymptotics (I): Poles
5.3 Analyticity and asymptotics (II): Algebraic singularities5.4 Analyticity and asymptotics (III): Hayman's method; Exercises; Solutions; References; Index
Summary: Generatingfunctionology
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
Online
QA353.G44 W55 2014 (Browse shelf) http://uttyler.eblib.com/patron/FullRecord.aspx?p=1888509 Available EBL1888509

Front Cover; Generatingfunctionology; Copyright Page; Preface; Table of Contents; Chapter 1. Introductory Ideas and Examples; 1.1 An easy two term recurrence; 1.2 A slightly harder two term recurrence; 1.3 A three term recurrence; 1.4 A three term boundary valueproblem; 1.5 Two independent variables; 1.6 Another 2-variable case; Exercises; Chapter 2. Series; 2.1 Formal power series; 2.2 The calculus of formal ordinary power seriesgenerating functions; 2.3 The calculus of formal exponential generating functions; 2.4 Power series, analytic theory; 2.5 Some useful power series

2.6 Dirichlet series, formal theoryExercises; Chapter 3. Cards, Decks, and Hands:The Exponential Formula; 3.1 Introduction; 3.2 Definitions and a question; 3.3 Examples of exponential families; 3.4 The main counting theorems; 3.5 Permutations and their cycles; 3.6 Set partitions; 3.7 A subclass of permutations; 3.8 Involutions, etc; 3.9 2-regular Graphs; 3.10 Counting connected graphs; 3.11 Counting labeled bipartite graphs; 3.12 Counting labeled trees; 3.13 Exponential families and polynomials of'binomial type.'; 3.14 Unlabeled cards and hands; 3.15 The money changing problem

3.16 Partitions of integers3.17 Rooted trees and forests; 3.18 Historical notes; Exercises; Chapter 4. Applications of Generating Functions; 4.1 Generating functions find averages, etc; 4.2 A generatingfunctionological view of the sieve method; 4.3 The 'Snake Oil' method for easier combinatorial identities; 4.4 WZ pairs prove harder identities; 4.5 Generating functions and unimodality, convexity, etc; 4.6 Generating functions prove congruences; Exercises; Chapter 5. Analytic and Asymptotic Methods; 5.1 The Lagrange Inversion Formula; 5.2 Analyticity and asymptotics (I): Poles

5.3 Analyticity and asymptotics (II): Algebraic singularities5.4 Analyticity and asymptotics (III): Hayman's method; Exercises; Solutions; References; Index

Generatingfunctionology

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