Principles and techniques in combinatorics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 298 S. graph. Darst. |
| ISBN: | 9810211392 9810211147 |
Internformat
MARC
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| 245 | 1 | 0 | |a Principles and techniques in combinatorics |c Chen Chuan-Chong and Koh Khee-Meng |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1992 | |
| 300 | |a XII, 298 S. |b graph. Darst. | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006510498 | ||
Datensatz im Suchindex
| _version_ | 1804124188837937152 |
|---|---|
| adam_text | Contents
Preface v
Notation and Abbreviation vii
Contents xi
1. Permutations and Combinations 1
1.1. Two Basic Counting Principles 1
1.2. Permutations 6
1.3. Circular Permutations 12
1.4. Combinations 17
1.5. The Injection and Bijection Principles 27
1.6. Arrangements and Selections with Repetitions 32
1.7. Distribution Problems 40
Exercise 1 50
2. Binomial Coefficients and Multinomial Coefficients .... 69
2.1. Introduction 69
2.2. The Binomial Theorem 70
2.3. Combinatorial Identities 71
2.4. The Pascal s Triangle 76
2.5. Chu Shih Chieh s Identity 78
2.6. Shortest Routes in a Rectangular Grid 85
2.7. Some Properties of Binomial Coefficients 93
2.8. Multinomial Coefficients and the Multinomial Theorem . . 96
Exercise 2 102
3. The Pigeonhole Principle and Ramsey Numbers 119
3.1. Introduction 119
3.2. The Pigeonhole Principle 119
3.3. More Examples 122
3.4. Ramsey Type Problems and Ramsey Numbers 129
3.5. Bounds for Ramsey Numbers 132
Exercise 3 137
xi
xii Contents
4. The Principle of Inclusion and Exclusion 145
4.1. Introduction 145
4.2. The Principle 146
4.3. A Generalization 148
4.4. Integer Solutions and Shortest Routes 153
4.5. Surjective Mappings and Stirling Numbers of the Second
Kind 158
4.6. Derangements and A Generalization 160
4.7. The Sieve of Eratosthenes and Euler y? function 163
4.8. The Trobleme des Menages 169
Exercise 4 173
5. Generating Functions 185
5.1. Ordinary Generating Functions 185
5.2. Some Modelling Problems 192
5.3. Partitions of Integers 196
5.4. Exponential Generating Functions 204
Exercise 5 211
6. Recurrence Relations 225
6.1. Introduction 225
6.2. Two Examples 228
6.3. Linear Homogeneous Recurrence Relations 234
6.4. General Linear Recurrence Relations 241
6.5. Two Applications 244
6.6. A System of Linear Recurrence Relations 251
6.7. The Method of Generating Functions 255
6.8. A Nonlinear Recurrence Relation and Catalan Numbers . . 259
6.9. Oscillating Permutations and an Exponential Generating
Function 262
Exercise 6 270
Bibliography 287
Answers 289
Index 297
|
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| id | DE-604.BV009833084 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:42Z |
| institution | BVB |
| isbn | 9810211392 9810211147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006510498 |
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| physical | XII, 298 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | World Scientific |
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| spelling | Chen, Chuan-Chong Verfasser aut Principles and techniques in combinatorics Chen Chuan-Chong and Koh Khee-Meng Singapore u.a. World Scientific 1992 XII, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 Kombinatorische Analysis (DE-588)4164746-4 s Koh, Khee-Meng Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006510498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Chuan-Chong Koh, Khee-Meng Principles and techniques in combinatorics Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4164746-4 |
| title | Principles and techniques in combinatorics |
| title_auth | Principles and techniques in combinatorics |
| title_exact_search | Principles and techniques in combinatorics |
| title_full | Principles and techniques in combinatorics Chen Chuan-Chong and Koh Khee-Meng |
| title_fullStr | Principles and techniques in combinatorics Chen Chuan-Chong and Koh Khee-Meng |
| title_full_unstemmed | Principles and techniques in combinatorics Chen Chuan-Chong and Koh Khee-Meng |
| title_short | Principles and techniques in combinatorics |
| title_sort | principles and techniques in combinatorics |
| topic | Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatorial analysis Kombinatorik Kombinatorische Analysis |
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