Book:Herbert S. Wilf/generatingfunctionology

Subject Matter

 * Generating Functions

Contents

 * Preface


 * Preface to the Second Edition


 * 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 value problem
 * 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 series generating 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 theory
 * Exercises


 * 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 integers
 * 3.17 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
 * 4.7 The cycle index of the symmetric group
 * 4.8 How many permutations have square roots?
 * 4.9 Counting polyominoes
 * 4.10 Exact covering sequences
 * 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 singularities
 * 5.4 Analyticity and asymptotics (III): Hayman's method
 * Exercises


 * Appendix: Using MapleTM and MathematicaTM


 * Solutions


 * References