Holdings: Generatingfunctionology

Generatingfunctionology:

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Bibliographic Details
Main Author:	Wilf, Herbert S. (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] Academic Press 1994
Edition:	2. ed.
Subjects:	Generating functions Erzeugende Funktion
Online Access:	Inhaltsverzeichnis
Physical Description:	IX, 228 S. graph. Darst.
ISBN:	0127519564

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MARC


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adam_text	CONTENTS Preface vii Preface to the Second Edition ix Chapter 1: Introductory Ideas and Examples 1.1 An easy two term recurrence 3 1.2 A slightly harder two term recurrence 5 1.3 A three term recurrence 8 1.4 A three term boundary value problem 10 1.5 Two independent variables 11 1.6 Another 2 variable case 16 Exercises 24 Chapter 2: Series 2.1 Formal power series 30 2.2 The calculus of formal ordinary power series generating functions 33 2.3 The calculus of formal exponential generating functions .... 39 2.4 Power series, analytic theory 46 2.5 Some useful power series 52 2.6 Dirichlet series, formal theory 56 Exercises 65 Chapter 3: Cards, Decks, and Hands: The Exponential Formula 3.1 Introduction 73 3.2 Definitions and a question 74 3.3 Examples of exponential families 76 3.4 The main counting theorems 78 3.5 Permutations and their cycles 81 3.6 Set partitions 83 3.7 A subclass of permutations 84 3.8 Involutions, etc 84 3.9 2 regular graphs 85 3.10 Counting connected graphs 86 3.11 Counting labeled bipartite graphs 87 3.12 Counting labeled trees 89 3.13 Exponential families and polynomials of binomial type. .... 91 3.14 Unlabeled cards and hands 92 3.15 The money changing problem 96 v vi Contents 3.16 Partitions of integers 100 3.17 Rooted trees and forests 102 3.18 Historical notes 103 Exercises 104 Chapter 4: Applications of generating functions 4.1 Generating functions find averages, etc 108 4.2 A generatingfunctionological view of the sieve method 110 4.3 The Snake Oil method for easier combinatorial identities . . .118 4.4 WZ pairs prove harder identities 130 4.5 Generating functions and unimodality, convexity, etc 136 4.6 Generating functions prove congruences 140 4.7 The cycle index of the symmetric group 141 4.8 How many permutations have square roots? 146 4.9 Counting polyominoes 150 4.10 Exact covering sequences 154 Exercises 157 Chapter 5: Analytic and asymptotic methods 5.1 The Lagrange Inversion Formula 167 5.2 Analyticity and asymptotics (I): Poles 171 5.3 Analyticity and asymptotics (II): Algebraic singularities .... 177 5.4 Analyticity and asymptotics (III): Hayman s method 181 Exercises 188 Appendix: Using Maple™ and Matliematica™ 192 Solutions 197 References 224 Index 227
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illustrated	Illustrated
indexdate	2024-07-09T17:42:00Z
institution	BVB
isbn	0127519564
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-006522109
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physical	IX, 228 S. graph. Darst.
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publisher	Academic Press
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spelling	Wilf, Herbert S. Verfasser aut Generatingfunctionology Herbert S. Wilf 2. ed. Boston [u.a.] Academic Press 1994 IX, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Generating functions gtt Generating functions Erzeugende Funktion (DE-588)4152979-0 gnd rswk-swf Erzeugende Funktion (DE-588)4152979-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006522109&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Wilf, Herbert S. Generatingfunctionology Generating functions gtt Generating functions Erzeugende Funktion (DE-588)4152979-0 gnd
subject_GND	(DE-588)4152979-0
title	Generatingfunctionology
title_auth	Generatingfunctionology
title_exact_search	Generatingfunctionology
title_full	Generatingfunctionology Herbert S. Wilf
title_fullStr	Generatingfunctionology Herbert S. Wilf
title_full_unstemmed	Generatingfunctionology Herbert S. Wilf
title_short	Generatingfunctionology
title_sort	generatingfunctionology
topic	Generating functions gtt Generating functions Erzeugende Funktion (DE-588)4152979-0 gnd
topic_facet	Generating functions Erzeugende Funktion
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006522109&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT wilfherberts generatingfunctionology

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