Principles of combinatorics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Acad. Press
1971
|
| Schriftenreihe: | Mathematics in science and engineering
72 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 176 S. |
| ISBN: | 0120897504 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Foreword vii
What Is Combinatorics?
First Aspect: Study of a Known Configuration 3
Second Aspect: Investigation of an Unknown Configuration 3
Third Aspect: Counting Configurations 5
Fourth Aspect: Approximate Counting of Configurations 7
Fifth Aspect: Enumeration of Configurations 8
Sixth Aspect: Optimization 9
References 10
1. The Elementary Counting Functions
1. Mappings of Finite Sets 13
2. The Cardinality of the Cartesian Product A x X 16
3. Number of Subsets of a Finite Set A 17
4. Numbers m , or Mappings of X into A 19
5. Number [m]n, or Injections of A1 into A 19
6. Numbers [m] 22
7. Numbers [m] ln , or Increasing Mappings of Xinto A 23
8. Binomial Numbers 25
/ n
9. Multinomial Numbers I I 32
hi , n2,¦¦¦, »p
10. Stirling Numbers Snm, or Partitions of n Objects
into m Classes 37
11. Bell Exponential Number Bn, or the Number of Partitions of n
Objects 42
References 44
2. Partition Problems
1. /V, or the Number of Partitions of Integer n into m Parts 47
2. Pn,h, or the Number of Partitions of the Integer n Having h as
the Smallest Part . 56
v
vi CONTENTS
3. Counting the Standard Tableaus Associated with a
Partition of n 59
4. Standard Tableaus and Young s Lattice 69
References 71
3. Inversion Formulas and Their Applications
1. Differential Operator Associated with a Family of
Polynomials 73
2. The Mobius Function 80
3. Sieve Formulas 88
4. Distributions 95
5. Counting Trees 99
References 109
4. Permutation Groups
1. Introduction 111
2. Cycles of a Permutation 119
3. Orbits of a Permutation Group 123
4. Parity of a Permutation 126
5. Decomposition Problems 139
References 147
5. Polya s Theorem
1. Counting Schemata Relative to a Group of Permutations
of Objects 149
2. Counting Schemata Relative to an Arbitrary Group 156
3. A Theorem of de Bruijn 164
4. Computing the Cycle Index 170
References 173
Index 175
|
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| id | DE-604.BV002625163 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:35Z |
| institution | BVB |
| isbn | 0120897504 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001686948 |
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| physical | VIII, 176 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Berge, Claude 1926-2002 Verfasser (DE-588)107792109 aut Principes de combinatoire Principles of combinatorics C. Berge New York u.a. Acad. Press 1971 VIII, 176 S. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 72 Grundlage (DE-588)4158388-7 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 Grundlage (DE-588)4158388-7 s Mathematics in science and engineering 72 (DE-604)BV000001196 72 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686948&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berge, Claude 1926-2002 Principles of combinatorics Mathematics in science and engineering Grundlage (DE-588)4158388-7 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4158388-7 (DE-588)4031824-2 |
| title | Principles of combinatorics |
| title_alt | Principes de combinatoire |
| title_auth | Principles of combinatorics |
| title_exact_search | Principles of combinatorics |
| title_full | Principles of combinatorics C. Berge |
| title_fullStr | Principles of combinatorics C. Berge |
| title_full_unstemmed | Principles of combinatorics C. Berge |
| title_short | Principles of combinatorics |
| title_sort | principles of combinatorics |
| topic | Grundlage (DE-588)4158388-7 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Grundlage Kombinatorik |
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