Principles and techniques in combinatorics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey u.a.
World Scientific
2007
|
| Edition: | Repr. paperback ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 298 S. Ill., graph. Darst. |
| ISBN: | 9810211392 9810211147 |
Staff View
MARC
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| 245 | 1 | 0 | |a Principles and techniques in combinatorics |c Chen Chuan-Chong and Koh Khee-Meng |
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| 264 | 1 | |a New Jersey u.a. |b World Scientific |c 2007 | |
| 300 | |a XII, 298 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804140991603539968 |
|---|---|
| adam_text | Contents
Preface
.................................
v
Notation
and Abbreviation
................... .
vii
Contents
................................ xi
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
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
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
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
уз
-function.......
163
4.8.
The
Probleme des
Ménages
..................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
|
| any_adam_object | 1 |
| author | Chen, Chuan-Chong Koh, Khee-Meng |
| author_facet | Chen, Chuan-Chong Koh, Khee-Meng |
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| author_sort | Chen, Chuan-Chong |
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| id | DE-604.BV035969592 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:08:46Z |
| institution | BVB |
| isbn | 9810211392 9810211147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018863627 |
| oclc_num | 553803162 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XII, 298 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Chen, Chuan-Chong Verfasser aut Principles and techniques in combinatorics Chen Chuan-Chong and Koh Khee-Meng Repr. paperback ed. New Jersey u.a. World Scientific 2007 XII, 298 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018863627&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 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 | Kombinatorik (DE-588)4031824-2 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Kombinatorik Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018863627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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