Fibonacci and catalan numbers: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, N.J.
Wiley
2012
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| Subjects: | |
| Online Access: | Cover image Publisher description Table of contents only Contributor biographical information Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 314 S. graph. Darst. |
| ISBN: | 9780470631577 |
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| 650 | 4 | |a Catalan numbers (Mathematics) | |
| 650 | 4 | |a Combinatorial analysis | |
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Record in the Search Index
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| adam_text | Titel: Fibonacci and Catalan numbers
Autor: Grimaldi, Ralph P
Jahr: 2012
CONTENTS
PREFACE xi
PART ONE THE FIBONACCI NUMBERS
1. Historical Background 3
2. The Problem of the Rabbits 5
3. The Recursive Definition 7
4. Properties of the Fibonacci Numbers 8
5. Some Introductory Examples 13
6. Compositions and Palindromes 23
7. Tilings: Divisibility Properties of the Fibonacci Numbers 33
8. Chess Pieces on Chessboards 40
9. Optics, Botany, and the Fibonacci Numbers 46
10. Solving Linear Recurrence Relations: The Binet Form for Fn 51
11. More on et and ß: Applications in Trigonometry, Physics, Continued
Fractions, Probability, the Associative Law, and Computer Science 65
12. Examples from Graph Theory: An Introduction to the Lucas Numbers 79
13. The Lucas Numbers: Further Properties and Examples 100
14. Matrices, The Inverse Tangent Function, and an Infinite Sum 113
15. The gcd Property for the Fibonacci Numbers 121
vii
Viii CONTENTS
16. Alternate Fibonacci Numbers 126
17. One Final Example? 140
PART TWO THE CATALAN NUMBERS
18. Historical Background 147
19. A First Example: A Formula for the Catalan Numbers 150
20. Some Further Initial Examples 159
21. Dyck Paths, Peaks, and Valleys 169
22. Young Tableaux, Compositions, and Vertices and Ares 183
23. Triangulating the Interior of a Convex Polygon 192
24. Some Examples from Graph Theory 195
25. Partial Orders, Total Orders, and Topological Sorting 205
26. Sequences and a Generating Tree 211
27. Maximal Cliques, a Computer Science Example, and the Tennis Ball
Problem 219
28. The Catalan Numbers at Sporting Events 226
29. A Recurrence Relation for the Catalan Numbers 231
30. Triangulating the Interior of a Convex Polygon for the Second Time 236
31. Rooted Ordered Binary Trees, Pattern Avoidance, and Data
Structures 238
32. Staircases, Arrangements of Coins, The Handshaking Problem, and
Noncrossing Partitions 250
33. The Narayana Numbers 268
34. Related Number Sequences: The Motzkin Numbers,
The Fine Numbers, and The Schröder Numbers 282
CONTENTS IX
35. Generalized Catalan Numbers 290
36. One Final Example? 296
Solutions for the Odd-Numbered Exercises 301
Index 355
|
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| dewey-full | 512.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/2 |
| dewey-search | 512.7/2 |
| dewey-sort | 3512.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| language | English |
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| spelling | Grimaldi, Ralph P. 1943- Verfasser (DE-588)1029529507 aut Fibonacci and catalan numbers an introduction Ralph P. Grimaldi Hoboken, N.J. Wiley 2012 XIV, 314 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Fibonacci numbers Recurrent sequences (Mathematics) Catalan numbers (Mathematics) Combinatorial analysis MATHEMATICS / Combinatorics bisacsh Fibonacci-Folge (DE-588)4249138-1 gnd rswk-swf Catalan-Vermutung (DE-588)4369060-9 gnd rswk-swf Fibonacci-Folge (DE-588)4249138-1 s Catalan-Vermutung (DE-588)4369060-9 s DE-604 http://catalogimages.wiley.com/images/db/jimages/9780470631577.jpg Cover image http://www.loc.gov/catdir/enhancements/fy1201/2011043338-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy1201/2011043338-t.html Table of contents only http://www.loc.gov/catdir/enhancements/fy1205/2011043338-b.html Contributor biographical information HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025014941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grimaldi, Ralph P. 1943- Fibonacci and catalan numbers an introduction Fibonacci numbers Recurrent sequences (Mathematics) Catalan numbers (Mathematics) Combinatorial analysis MATHEMATICS / Combinatorics bisacsh Fibonacci-Folge (DE-588)4249138-1 gnd Catalan-Vermutung (DE-588)4369060-9 gnd |
| subject_GND | (DE-588)4249138-1 (DE-588)4369060-9 |
| title | Fibonacci and catalan numbers an introduction |
| title_auth | Fibonacci and catalan numbers an introduction |
| title_exact_search | Fibonacci and catalan numbers an introduction |
| title_full | Fibonacci and catalan numbers an introduction Ralph P. Grimaldi |
| title_fullStr | Fibonacci and catalan numbers an introduction Ralph P. Grimaldi |
| title_full_unstemmed | Fibonacci and catalan numbers an introduction Ralph P. Grimaldi |
| title_short | Fibonacci and catalan numbers |
| title_sort | fibonacci and catalan numbers an introduction |
| title_sub | an introduction |
| topic | Fibonacci numbers Recurrent sequences (Mathematics) Catalan numbers (Mathematics) Combinatorial analysis MATHEMATICS / Combinatorics bisacsh Fibonacci-Folge (DE-588)4249138-1 gnd Catalan-Vermutung (DE-588)4369060-9 gnd |
| topic_facet | Fibonacci numbers Recurrent sequences (Mathematics) Catalan numbers (Mathematics) Combinatorial analysis MATHEMATICS / Combinatorics Fibonacci-Folge Catalan-Vermutung |
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