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Proofs that really count: the art of combinatorial proof

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Bibliographic Details
Main Authors:	Benjamin, Arthur T. 1961- (Author), Quinn, Jennifer J. (Author)
Format:	Book
Language:	English
Published:	Washington, DC Math. Assoc. of America 2003
Series:	The Dolciani mathematical expositions 27
Subjects:	Beweis - Kombinatorische Analysis Combinatorial analysis Kombinatorik Mathematik Beweis Einführung
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
Physical Description:	XIV, 194 S. Ill., graph. Darst.
ISBN:	0883853337

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Record in the Search Index

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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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isbn	0883853337
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series	The Dolciani mathematical expositions
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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
volume_link	(DE-604)BV001900740
work_keys_str_mv	AT benjaminarthurt proofsthatreallycounttheartofcombinatorialproof AT quinnjenniferj proofsthatreallycounttheartofcombinatorialproof

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