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Fibonacci and Catalan numbers : an introduction

Author: Ralph P Grimaldi
Publisher: Hoboken, N.J. : John Wiley & Sons, ©2012.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers. The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ralph P Grimaldi
ISBN: 9780470631577 0470631570
OCLC Number: 744299345
Description: xiv, 366 pages : illustrations ; 24 cm
Contents: Part One: The Fibonacci Numbers. Historical Background --
The Problem of the Rabbits --
The Recursive Definition --
Properties of the Fibonacci Numbers --
Some Introductory Ecamples --
Compositions and Palindromes --
Tilings: Divisibility Properties of the Fibonacci Numbers --
Chess Pieces on Chessboards --
Optics, Botany, and the Fibonacci Numbers --
Solving Linear Recurrence Relations: The Binet Form for Fn --
More on a and B: Applications to Trigonometry, Physics, Continued Fracts, Probability, the Associative Law, and Computer Science --
Examples from Graph Theory: An Introduction to the Lucas Numbers --
The Lucas Numbers: Further Properties and Examples --
Matrices, The Inverse Tangent FUnction, and an Infinitive Sum --
The gcd Property for the Fibonacci Numbers --
Alternate Fibonacci Numbers --
One Final Example? --
Part Two: The Catalan Numbers. Historical Background --
A First Example: A Formula for the Catalan Numbers --
Some Further Initial Examples --
Dyck Paths, Peaks, and Valleys --
Young Tableaux, Compositions, and Vertices and Arcs --
Triangulating the Interior of a Convex Polygon --
Some Examples from Graph Theory --
Partial Orders, Total Orders, and Topological Sorting --
Sequences and a Generating Tree --
Maximal Cliques, a Computer Science Example, and the Tennis Ball Problem --
The Catalan Numbers at Sporting Events --
A Recurrence Relation for the Catalan Numbers --
Triangulating the Interior of a Convex Polygon for the Second Time --
Rooted Ordered Binary Trees, Pattern Avoidance, and Data Structures --
Staircases, Arrangements of Coins, The Handshaking Problem, and Noncrossing Partitions --
The Narayana Numbers --
Related Number Sequences: The Motzkin Numbers, The Fine Numbers, and the Schroder Numbers --
Generalized Catalan Numbers --
One Final Example?
Responsibility: Ralph P. Grimaldi.
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Abstract:

The material has been extensively class-tested for over ten years at both the author's own university and other institutions. The book is uniquely organized into two main sections, one on  Read more...

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