Generatingfunctionology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Academic Press
1994
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 228 S. graph. Darst. |
| ISBN: | 0127519564 |
Internformat
MARC
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| 100 | 1 | |a Wilf, Herbert S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generatingfunctionology |c Herbert S. Wilf |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Academic Press |c 1994 | |
| 300 | |a IX, 228 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Generating functions | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006522109 | ||
Datensatz im Suchindex
| _version_ | 1804124207408218112 |
|---|---|
| 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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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV009852962 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:42:00Z |
| institution | BVB |
| isbn | 0127519564 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006522109 |
| oclc_num | 29831213 |
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| physical | IX, 228 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Academic Press |
| record_format | marc |
| 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 |
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