Proofs that really count: the art of combinatorial proof
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Washington, DC
Math. Assoc. of America
2003
|
| Schriftenreihe: | The Dolciani mathematical expositions
27 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010771554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 194 S. Ill., graph. Darst. |
| ISBN: | 0883853337 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Proofs that really count
Autor: Benjamin, Arthur T.
Jahr: 2003
Contents
Foreword ix
1 Fibonacci Identities 1
1.1 Combinatorial Interpretation of Fibonacci Numbers............. 1
1.2 Identities.................................... 2
1.3 A Fun Application.............................. 11
1.4 Notes ..................................... 12
1.5 Exercises ................................... 13
2 Gibonacci and Lucas Identities 17
2.1 Combinatorial Interpretation of Lucas Numbers............... 17
2.2 Lucas Identities................................ 18
2.3 Combinatorial Interpretation of Gibonacci Numbers ............ 23
2.4 Gibonacci Identities.............................. 23
2.5 Notes ..................................... 32
2.6 Exercises ................................... 32
3 Linear Recurrences 35
3.1 Combinatorial Interpretations of Linear Recurrences............ 36
3.2 Identities for Second-Order Recurrences................... 38
3.3 Identities for Third-Order Recurrences.................... 40
3.4 Identities for kth Order Recurrences..................... 43
3.5 Get Real! Arbitrary Weights and Initial Conditions............. 44
3.6 Notes ..................................... 45
3.7 Exercises ................................... 45
4 Continued Fractions 49
4.1 Combinatorial Interpretation of Continued Fractions............ 49
4.2 Identities.................................... 52
4.3 Nonsimple Continued Fractions....................... 58
4.4 Get Real Again!................................ 59
4.5 Notes ..................................... 59
4.6 Exercises ................................... 60
xiii
xiv PROOFS THAT REALLY COUNT
5 Binomial Identities 63
5.1 Combinatorial Merpretations of Binomial Coefficients........... 63
5.2 Elementary Identities............................. 64
5.3 More Binomial Coefficient Identities .................... 68
5.4 Multichoosing................................. 70
5.5 Odd Numbers in Pascal s Triangle...................... 75
5.6 Notes ..................................... 77
5.7 Exercises ................................... 78
6 Alternating Sign Binomial Identities 81
6.1 Parity Arguments and Inclusion-Exclusion.................. 81
6.2 Alternating Binomial Coefficient Identities................. 84
6.3 Notes ..................................... 89
6.4 Exercises ................................... 89
7 Harmonic and Stirling Number Identities 91
7.1 Harmonic Numbers and Permutations....................91
7.2 Stirling Numbers of the First Kind......................93
7.3 Combinatorial Interpretation of Harmonic Numbers............. 97
7.4 Recounting Harmonic Identities.......................98
7.5 Stirling Numbers of the Second Kind....................103
7.6 Notes .....................................106
7.7 Exercises ...................................106
8 Number Theory 109
8.1 Arithmetic Identities .............................109
8.2 Algebra and Number Theory.........................114
8.3 GCDs Revisited................................118
8.4 Lucas Theorem................................120
8.5 Notes .....................................123
8.6 Exercises ...................................123
9 Advanced Fibonacci Lucas Identities 125
9.1 More Fibonacci and Lucas Identities.....................125
9.2 Colorful Identities...............................130
9.3 Some Random Identities and the Golden Ratio..............136
9.4 Fibonacci and Lucas Polynomials......................141
9.5 Negative Numbers ..............................143
9.6 Open Problems and Vajda Data.......................143
Some Hints and Solutions for Chapter Exercises 147
Appendix of Combinatorial Theorems 171
Appendix of Identities 173
Bibliography 187
Index 191
About the Authors 194
|
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| genre_facet | Einführung |
| id | DE-604.BV017978017 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:25:15Z |
| institution | BVB |
| isbn | 0883853337 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010771554 |
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| physical | XIV, 194 S. Ill., graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Math. Assoc. of America |
| record_format | marc |
| series | The Dolciani mathematical expositions |
| series2 | The Dolciani mathematical expositions |
| spellingShingle | Benjamin, Arthur T. 1961- Quinn, Jennifer J. Proofs that really count the art of combinatorial proof The Dolciani mathematical expositions Beweis - Kombinatorische Analysis Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4037944-9 (DE-588)4132532-1 (DE-588)4151278-9 |
| title | Proofs that really count the art of combinatorial proof |
| title_auth | Proofs that really count the art of combinatorial proof |
| title_exact_search | Proofs that really count the art of combinatorial proof |
| title_full | Proofs that really count the art of combinatorial proof Arthur T. Benjamin and Jennifer J. Quinn |
| title_fullStr | Proofs that really count the art of combinatorial proof Arthur T. Benjamin and Jennifer J. Quinn |
| title_full_unstemmed | Proofs that really count the art of combinatorial proof Arthur T. Benjamin and Jennifer J. Quinn |
| title_short | Proofs that really count |
| title_sort | proofs that really count the art of combinatorial proof |
| title_sub | the art of combinatorial proof |
| topic | Beweis - Kombinatorische Analysis Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Beweis - Kombinatorische Analysis Combinatorial analysis Kombinatorik Mathematik Beweis Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010771554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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