Principles and techniques in combinatorics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u. a.]
World Scient.
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 298 Seiten |
| ISBN: | 9810211392 |
Internformat
MARC
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| 245 | 1 | 0 | |a Principles and techniques in combinatorics |c Chen Chuan-Chong; Koh Khee-Meng |
| 264 | 1 | |a Singapore [u. a.] |b World Scient. |c 1992 | |
| 300 | |a XII, 298 Seiten | ||
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| 776 | 0 | 8 | |i Solutions manual u.d.T.: |a Foo, Kean Pew |t Principles and techniques in combinatorics |
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Datensatz im Suchindex
| _version_ | 1804141343218335744 |
|---|---|
| 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 MultinomialCoefficients .... 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
4. The 4.1. 4.2. 4.3. 4.4. 4.5. Principle of Inclusion and Exclusion............................. 145 Introduction................................................................................ 145 The Principle..............................................................................146 A Generalization........................................................................ 148 Integer Solutions and Shortest Routes.................................... 153 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 ^-function................... 163 4.8. The ‘Probléme 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
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| any_adam_object | 1 |
| author | Chen, Chuan-Chong Koh, Khee-Meng |
| author_facet | Chen, Chuan-Chong Koh, Khee-Meng |
| author_role | aut aut |
| author_sort | Chen, Chuan-Chong |
| author_variant | c c c ccc k m k kmk |
| building | Verbundindex |
| bvnumber | BV025883810 |
| classification_rvk | SK 170 |
| ctrlnum | (OCoLC)832172967 (DE-599)BVBBV025883810 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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.BV025883810 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:14:22Z |
| institution | BVB |
| isbn | 9810211392 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019130585 |
| oclc_num | 832172967 |
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| owner_facet | DE-11 DE-739 |
| physical | XII, 298 Seiten |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | World Scient. |
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| spelling | Chen, Chuan-Chong Verfasser aut Principles and techniques in combinatorics Chen Chuan-Chong; Koh Khee-Meng Singapore [u. a.] World Scient. 1992 XII, 298 Seiten txt rdacontent n rdamedia nc rdacarrier Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 Kombinatorische Analysis (DE-588)4164746-4 s Koh, Khee-Meng Verfasser aut Solutions manual u.d.T.: Foo, Kean Pew Principles and techniques in combinatorics Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019130585&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Chuan-Chong Koh, Khee-Meng Principles and techniques in combinatorics Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4031824-2 |
| 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; Koh Khee-Meng |
| title_fullStr | Principles and techniques in combinatorics Chen Chuan-Chong; Koh Khee-Meng |
| title_full_unstemmed | Principles and techniques in combinatorics Chen Chuan-Chong; Koh Khee-Meng |
| title_short | Principles and techniques in combinatorics |
| title_sort | principles and techniques in combinatorics |
| topic | Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Kombinatorische Analysis Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019130585&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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