An introduction to combinatorics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Chapman & Hall
1991
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Chapman & Hall mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 266 |
| Beschreibung: | XV, 270 S. |
| ISBN: | 0412353601 |
Internformat
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| 245 | 1 | 0 | |a An introduction to combinatorics |c Alan Slomson |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London u.a. |b Chapman & Hall |c 1991 | |
| 300 | |a XV, 270 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction xi
Why combinatorics? xi
Counting problems xii
What you need to know xiii
Are you sitting comfortably? xiv
Acknowledgements xv
1 Permutations and combinations 1
1.1 Introduction 1
1.2 Permutations 1
1.3 Combinations 5
1.4 Applications to probability problems 11
2 The inclusion exclusion principle 19
2.1 Double counting 19
2.2 Derangements 25
3 Partitions 29
3.1 What are partitions? 29
3.2 Dot diagrams 32
3.3 What is a formula? 36
3.4 A lower bound for pk(n) 40
4 Stirling s approximation 43
4.1 Asymptotic functions 43
4.2 Stirling s formula 47
4.3 A note on James Stirling 54
4.4 A lower bound for p(n) 55
viii Contents
5 Partitions and generating functions 58
5.1 Introduction 58
5.2 Generating functions 62
5.3 Applications to partition numbers 66
5.4 Euler s identity 70
5.5 The Hardy Ramanujan formula 73
5.6 The story of Hardy and Ramanujan 76
6 Generating functions and recurrence relations 80
6.1 What is a recurrence relation? 80
6.2 The use of generating functions 82
6.3 Homogeneous linear recurrence relations 86
6.4 Inhomogenous linear recurrence relations 93
6.5 Some non linear recurrence relations 100
6.6 Partial fractions 104
7 Permutations and groups 109
7.1 Permutations 109
7.2 Groups of permutations 113
7.3 Symmetry groups 120
7.4 Subgroups and Lagrange s Theorem 123
7.5 Orders of group elements 129
7.6 The orders of permutations 131
8 Group actions 136
8.1 Colourings 136
8.2 The axioms for group actions 139
8.3 Orbits 142
8.4 Stabilizers 144
9 Graphs 150
9.1 What are graphs? 150
9.2 Labelled graphs 154
10 Counting patterns 158
10.1 Burnside s Theorem 158
10.2 Applications of Burnside s Theorem 160
11 Polya s Theorem 167
11.1 Colourings and group actions 167
11.2 Pattern inventories 170
11.3 The cycle index of a group 173
11.4 Polya s Theorem: statement and examples 177
11.5 Polya s Theorem: the proof 181
Contents ix
11.6 Counting simple graphs 185
11.7 Conclusion 193
Supplementary exercises 194
Solutions 203
Suggestions for further reading 265
List of special symbols 267
Index 269
|
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| author | Slomson, Alan B. 1943- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T17:08:33Z |
| institution | BVB |
| isbn | 0412353601 |
| language | English |
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| physical | XV, 270 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Chapman & Hall |
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| series2 | Chapman & Hall mathematics |
| spelling | Slomson, Alan B. 1943- Verfasser (DE-588)144005565 aut An introduction to combinatorics Alan Slomson 1. ed. London u.a. Chapman & Hall 1991 XV, 270 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall mathematics Literaturverz. S. 266 Analise Combinatoria larpcal Analyse combinatoire Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005082534&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Slomson, Alan B. 1943- An introduction to combinatorics Analise Combinatoria larpcal Analyse combinatoire Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4031824-2 |
| title | An introduction to combinatorics |
| title_auth | An introduction to combinatorics |
| title_exact_search | An introduction to combinatorics |
| title_full | An introduction to combinatorics Alan Slomson |
| title_fullStr | An introduction to combinatorics Alan Slomson |
| title_full_unstemmed | An introduction to combinatorics Alan Slomson |
| title_short | An introduction to combinatorics |
| title_sort | an introduction to combinatorics |
| topic | Analise Combinatoria larpcal Analyse combinatoire Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Analise Combinatoria Analyse combinatoire Combinatieleer Combinatorial analysis Kombinatorik |
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