Introduction to combinatorics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2013
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in discrete mathematics and optimization
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index Weitere Ausgabe: Online version : Introduction to combinatorics |
| Beschreibung: | XII, 230 S. graph. Darst. |
| ISBN: | 9781118637531 9781118640210 |
Internformat
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| 245 | 1 | 0 | |a Introduction to combinatorics |c Martin J. Erickson |
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| 300 | |a XII, 230 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in discrete mathematics and optimization | |
| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
| _version_ | 1804150472762720256 |
|---|---|
| adam_text | Titel: Introduction to combinatorics
Autor: Erickson, Martin J
Jahr: 2013
CONTENTS
Preface xi
1 Basic Counting Methods 1
1.1 The multiplication principle 1
1.2 Permutations 4
1.3 Combinations 6
1.4 Binomial coefficient identities 11
1.5 Distributions 20
1.6 The principle of inclusion and exclusion 23
1.7 Fibonacci numbers 31
1.8 Linear recurrence relations 34
1.9 Special recurrence relations 40
1.10 Counting and number theory 45
Notes 50
2 Generating Functions 53
2.1 Rational generating functions 53
2.2 Special generating functions 63
2.3 Partition numbers 76
2.4 Labeled and unlabeled sets 80
2.5 Counting with symmetry 85
2.6 Cycle indexes 92
2.7 Polya s theorem 95
2.8 The number of graphs 98
2.9 Symmetries in domain and range 102
2.10 Asymmetric graphs 104
Notes 105
3 The Pigeonhole Principle 107
3.1 The principle 107
3.2 The lattice point problem and SET® 110
3.3 Graphs 114
3.4 Colorings of the plane 118
3.5 Sequences and partial orders 119
3.6 Subsets 124
Notes 126
4 Ramsey Theory 131
4.1 Ramsey s theorem 131
4.2 Generalizations of Ramsey s theorem 135
4.3 Ramsey numbers, bounds, and asymptotics 139
4.4 The probabilistic method 142
4.5 Schur s theorem 145
4.6 Van der Waerden s theorem 146
Notes 150
5 Error-Correcting Codes 153
5.1 Binary codes 153
5.2 Perfect codes 156
5.3 Hamming codes 158
5.4 The Fano Configuration 162
Notes 168
6 Combinatorial Designs 171
6.1 ^-designs 171
6.2 Block designs 175
6.3 Projective planes 180
6.4 Latin squares 183
6.5 MOLSandOODs 185
6.6 Hadamard matrices 189
6.7 The Golay code and 5(5,8, 24) 194
6.8 Lattices and sphere packings 197
6.9 Leech s lattice 200
Notes 202
A Web Resources 205
B Notation 207
Exercise Solutions 211
References 223
Index 225
|
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| dewey-sort | 3511 16 |
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| discipline | Mathematik |
| edition | 2. ed. |
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| language | English |
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| physical | XII, 230 S. graph. Darst. |
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| spelling | Erickson, Martin J. 1963-2013 Verfasser (DE-588)139664181 aut Introduction to combinatorics Martin J. Erickson 2. ed. Hoboken, NJ Wiley 2013 XII, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in discrete mathematics and optimization Includes bibliographical references and index Weitere Ausgabe: Online version : Introduction to combinatorics Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Kombinatorik (DE-588)4031824-2 s DE-604 http://catalogimages.wiley.com/images/db/jimages/9781118637531.jpg Cover HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026071615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Introduction to combinatorics |
| title_auth | Introduction to combinatorics |
| title_exact_search | Introduction to combinatorics |
| title_full | Introduction to combinatorics Martin J. Erickson |
| title_fullStr | Introduction to combinatorics Martin J. Erickson |
| title_full_unstemmed | Introduction to combinatorics Martin J. Erickson |
| title_short | Introduction to combinatorics |
| title_sort | introduction to combinatorics |
| topic | Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Combinatorial analysis Kombinatorik Einführung |
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