Fibonacci and catalan numbers : an introduction /

• Κύριος συγγραφέας: Grimaldi, Ralph P.
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Hoboken, N.J. : John Wiley & Sons, [2012]
• Θέματα: Fibonacci numbers.; Recurrent sequences (Mathematics); Catalan numbers (Mathematics); Combinatorial analysis.; MATHEMATICS > Combinatorics.; Electronic books.

"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. Sta...

Πίνακας περιεχομένων:

• Frontmatter
• The Fibonacci Numbers. Historical Background
• The Problem of the Rabbits
• The Recursive Definition
• Properties of the Fibonacci Numbers
• Some Introductory Examples
• 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
• More on and : Applications in Trigonometry, Physics, Continued Fractions, 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 Infinite Sum
• The gcd Property for the Fibonacci Numbers
• Alternate Fibonacci Numbers
• One Final Example?
• 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 Schr̲der Numbers
• Generalized Catalan Numbers
• One Final Example?
• Solutions for the Odd-Numbered Exercises
• Index.