Counting: the art of enumerative combinatorics:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009455269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 250 S. graph. Darst. |
| ISBN: | 038795225X |
Internformat
MARC
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| 245 | 1 | 0 | |a Counting: the art of enumerative combinatorics |c George E. Martin |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XI, 250 S. |b graph. Darst. | ||
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| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 4 | |a Abzählende Kombinatorik | |
| 650 | 4 | |a Combinatorial enumeration problems | |
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Datensatz im Suchindex
| _version_ | 1819266159407529984 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Elementary Enumeration
§1. Counting Is Hard 1
§2. Conventions 2
§3. Permutations 3
§4. A Discussion Question 4
§5. The Pigeonhole Principle 4
§6. n Chose r by Way of MISSISSIPPI 5
§7. The Round Table 7
§8. The Birthday Problem 10
§9. n Chose r with Repetition 11
§10. Ice Cream Cones—The Double Dip 17
§11. Block Walking 18
§12. Quickies and Knights 19
§13. The Binomial Theorem 22
§14. Homework for a Week 23
§15. Three Hour Exams 24
Chapter 2. The Principle of Inclusion and Exclusion
§16. Introduction to PIE 27
§17. Proof of PIE 30
§ 18. Derangements 32
x Contents
§19. Partitions 34
§20. Balls into Boxes 35
§21. A Plethora of Problems 38
§22. Eating Out 39
Chapter 3. Generating Functions
§23. What Is x? 43
§24. An Algebraic Excursion to R[[x]] 44
§25. Introducing Generating Functions 46
§26. Clotheslines 47
§27. Examples and Homework 52
§28. Computations 57
§29. Exponential Generating Functions 59
§30. Comprehensive Exams 64
Chapter 4. Groups
§31. Symmetry Groups 67
§32. Legendre s Theorem 71
§33. Permutation Groups 74
§34. Generators 77
§35. Cyclic Groups 80
§36. Equivalence and Isomorphism 82
Chapter 5. Actions
§37. The Definition 85
§38. Burnside s Lemma 88
§39. Applications of Burnside s Lemma 94
§40. Polya s Pattern Inventory 100
§41. Necklaces 108
Chapter 6. Recurrence Relations
§42. Examples of Recurrence Relations 113
§43. The Fibonacci Numbers 117
§44. A Dozen Recurrence Problems 121
§45. Solving Recurrence Relations 122
§46. The Catalan Numbers 125
§47. Nonhomogeneous Recurrence Relations 133
Contents xi
Chapter 7. Mathematical Induction
§48. The Principle of Mathematical Induction 137
§49. The Strong Form of Mathematical Induction 142
§50. Hall s Marriage Theorem 146
Chapter 8. Graphs
§51. The Vocabulary of Graph Theory 153
§52. Walks, Trails, Circuits, Paths, and Cycles 160
§53. Trees 168
§54. Degree Sequences 175
§55. Euler s Formula 177
The Back of the Book 183
Index 247
|
| any_adam_object | 1 |
| author | Martin, George E. 1932- |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.62 |
| dewey-search | 511.62 |
| dewey-sort | 3511.62 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013826153 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:54:13Z |
| institution | BVB |
| isbn | 038795225X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009455269 |
| oclc_num | 248188624 |
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| physical | XI, 250 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spellingShingle | Martin, George E. 1932- Counting: the art of enumerative combinatorics Abzählende Kombinatorik Combinatorial enumeration problems Abzählende Kombinatorik (DE-588)4132720-2 gnd |
| subject_GND | (DE-588)4132720-2 |
| title | Counting: the art of enumerative combinatorics |
| title_auth | Counting: the art of enumerative combinatorics |
| title_exact_search | Counting: the art of enumerative combinatorics |
| title_full | Counting: the art of enumerative combinatorics George E. Martin |
| title_fullStr | Counting: the art of enumerative combinatorics George E. Martin |
| title_full_unstemmed | Counting: the art of enumerative combinatorics George E. Martin |
| title_short | Counting: the art of enumerative combinatorics |
| title_sort | counting the art of enumerative combinatorics |
| topic | Abzählende Kombinatorik Combinatorial enumeration problems Abzählende Kombinatorik (DE-588)4132720-2 gnd |
| topic_facet | Abzählende Kombinatorik Combinatorial enumeration problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009455269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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