Introduction to combinatorics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2011
|
| Schriftenreihe: | Discrete mathematics and its applications
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 380 S. graph. Darst. |
| ISBN: | 9781439806227 |
Internformat
MARC
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| 020 | |a 9781439806227 |c (hbk.) : 49.99 GBP |9 978-1-4398-0622-7 | ||
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| 245 | 1 | 0 | |a Introduction to combinatorics |c W. D. Wallis ; J. C. George |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XVI, 380 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Discrete mathematics and its applications | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a Kombinatorik |0 (DE-588)4031824-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kombinatorik |0 (DE-588)4031824-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a George, John C. |d 1959- |e Verfasser |0 (DE-588)142484288 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-018628505 | |
Datensatz im Suchindex
| _version_ | 1819351502129463296 |
|---|---|
| adam_text | Contents
List of Figures
xiii
Preface
xv
1
Introduction
1
1.1
Some Combinatorial Examples
................. 1
1.2
Sets, Relations and Proof Techniques
............. 13
1.3
Two Principles of Enumeration
................. 15
1.4
Graphs
.............................. 18
1.5
Systems of Distinct Representatives
.............. 20
Exercises 1A
........................... 22
Exercises IB
........................... 23
Problems
............................. 25
2
Fundamentals of Enumeration
27
2.1
Permutations and Combinations
................ 27
2.2
Applications of P(n, k) and
)................ 29
2.3
Permutations and Combinations of Multisets
......... 32
2.4
Applications and Subtle Errors
................. 36
2.5
Algorithms
............................ 39
Exercises 2A
........................... 41
Exercises 2B
........................... 43
Problems
............................. 44
3
The Pigeonhole Principle and Ramsey s Theorem
47
3.1
The Pigeonhole Principle
.................... 47
3.2
Applications of the Pigeonhole Principle
........... 48
3.3
Ramsey s Theorem
—
the Graphical Case
........... 51
3.4
Ramsey Multiplicity
....................... 54
3.5
Sum-Free Sets
.......................... 56
3.6
Bounds on Ramsey Numbers
.................. 59
3.7
The General Form of Ramsey s Theorem
........... 63
Exercises
ЗА
........................... 63
Exercises 3B
........................... 64
Problems
............................. 66
ix
The Principle of Inclusion and Exclusion
69
4.1
Unions of Events
......................... 69
4.2
The Principle
........................... 71
4.3
Combinations with Limited Repetitions
............ 75
4.4
Derangements
.......................... 77
Exercises 4A
........................... 80
Exercises 4B
........................... 81
Problems
............................. 83
Generating Functions and Recurrence Relations
85
5.1
Generating Functions
...................... 85
5.2
Recurrence Relations
...................... 89
5.3
From Generating Function to Recurrence
........... 94
5.4
Exponential Generating Functions
............... 95
Exercises 5A
........................... 97
Exercises 5B
........................... 99
Problems
............................. 100
Catalan, Bell and Stirling Numbers
103
6.1
Introduction
........................... 103
6.2
Catalan Numbers
........................ 104
6.3
Stirling Numbers of the Second Kind
............. 108
6.4
Bell Numbers
........................... 113
6.5
Stirling Numbers of the First Kind
............... 114
6.6
Computer Algebra and Other Electronic Systems
...... 117
Exercises 6A
........................... 119
Exercises 6B
........................... 121
Problems
............................. 122
Symmetries and the
Pólya-Redfield
Method
123
7.1
Introduction
........................... 123
7.2
Basics of Groups
......................... 124
7.3
Permutations and Colorings
.................. 130
7.4
An Important Counting Theorem
............... 131
7.5
Pólya
and Redfield s Theorem
................. 134
Exercises 7A
........................... 138
Exercises 7B
........................... 139
Problems
............................. 140
Introduction to Graph Theory
143
8.1
Degrees
.............................. 143
8.2
Paths and Cycles in Graphs
.................. 146
8.3
Maps and Graph Coloring
................... 149
Exercises 8A
........................... 153
Exercises 8B
........................... 155
Problems
............................. 156
Xl
9
Further Graph Theory
159
9.1
Euler
Walks and Circuits
.................... 159
9.2
Application of
Euler
Circuits to Mazes
............ 164
9.3
Hamilton Cycles
......................... 166
9.4
Trees
............................... 170
9.5
Spanning Trees
.......................... 174
Exercises 9A
........................... 180
Exercises 9B
........................... 184
Problems
............................. 187
10
Coding Theory
189
10.1
Errors; Noise
........................... 189
10.2
The Venn Diagram Code
.................... 190
10.3
Binary Codes; Weight; Distance
................ 192
10.4
Linear Codes
........................... 195
10.5
Hamming Codes
......................... 198
10.6
Codes and the Hat Problem
.................. 200
10.7
Variable-Length Codes and Data Compression
........ 201
Exercises 10A
.......................... 203
Exercises 10B
.......................... 204
Problems
............................. 205
11
Latin Squares
207
11.1
Introduction
........................... 207
11.2
Orthogonality
.......................... 211
11.3
Idempotent Latin Squares
.................... 217
11.4
Partial Latin Squares and
Subsquares
............. 219
11.5
Applications
........................... 221
Exercises 11A
.......................... 225
Exercises 11B
.......................... 228
Problems
............................. 229
12
Balanced Incomplete Block Designs
231
12.1
Design Parameters
........................ 232
12.2
Fisheťs
Inequality
........................ 236
12.3
Symmetric Balanced Incomplete Block Designs
........ 238
12.4
New Designs from Old
..................... 240
12.5
Difference Methods
....................... 242
Exercises 12A
.......................... 245
Exercises 12B
.......................... 247
Problems
............................. 248
Xli
13
Linear Algebra
Methods in Combinatorics
251
13.1
Recurrences Revisited
...................... 251
13.2
State Graphs and the Transfer Matrix Method
........ 253
13.3
Kasteleyn s Permanent Method
................ 260
Exercises 13A
.......................... 265
Exercises 13B
.......................... 267
Problems
............................. 268
Appendix
1:
Sets; Proof Techniques
271
Al.l Sets and Basic Set Operations
................. 271
Al.
2
The Principle of Mathematical Induction
........... 279
A1.3 Some Applications of Induction
................ 281
A1.4 Binary Relations on Sets
.................... 283
Exercises A
........................... 285
Exercises
В
........................... 286
Appendix
2:
Matrices and Vectors
291
A2.1 Definitions
............................ 291
A2.2 Vector and Matrix Products
.................. 294
A2.3 Inverses
.............................. 296
A2.4 Determinants
.......................... 298
Exercises A
........................... 299
Exercises
В
........................... 301
Appendix
3:
Some Combinatorial People
305
Solutions to Set A Exercises
313
Hints for Problems
341
Solutions to Problems
347
References
367
Index
375
|
| any_adam_object | 1 |
| author | Wallis, Walter D. 1941- George, John C. 1959- |
| author_GND | (DE-588)135619173 (DE-588)142484288 |
| author_facet | Wallis, Walter D. 1941- George, John C. 1959- |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035768764 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:59:45Z |
| institution | BVB |
| isbn | 9781439806227 |
| language | English |
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| physical | XVI, 380 S. graph. Darst. |
| publishDate | 2011 |
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| publisher | CRC Press |
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| series2 | Discrete mathematics and its applications |
| spellingShingle | Wallis, Walter D. 1941- George, John C. 1959- Introduction to combinatorics Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4031824-2 |
| title | Introduction to combinatorics |
| title_auth | Introduction to combinatorics |
| title_exact_search | Introduction to combinatorics |
| title_full | Introduction to combinatorics W. D. Wallis ; J. C. George |
| title_fullStr | Introduction to combinatorics W. D. Wallis ; J. C. George |
| title_full_unstemmed | Introduction to combinatorics W. D. Wallis ; J. C. George |
| title_short | Introduction to combinatorics |
| title_sort | introduction to combinatorics |
| topic | Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Combinatorial analysis Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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