Fibonacci and Catalan Numbers An Introduction – Ralph P. Grimaldi – 1st Edition


With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers.

Beginning with a historical development of each topic, the guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci to compositions and palindromes, tilings, graph theory, and the Lucas numbers.

The proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers.

The features various aids and insights that allow readers to develop a complete understanding of the presented topics, including:

– Real-world examples that demonstrate the application of the Fibonacci and the Catalan to such fields as sports, botany, chemistry, physics, and computer science

– More than 300 exercises that enable readers to explore many of the presented examples in greater depth

– Illustrations that clarify and simplify the concepts

Fibonacci and Catalan is an excellent for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.

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Table of Contents

Part one - The fibonacci numbers
1. Historical background
2. The problem of the rabbits
3. The recursive definition
4. Properties of the fibonacci numbers
5. Some introductory examples
6. Compositions and palindromes
7. Tilings: Divisibility properties of the fibonacci numbers
8. Chess pieces on chessboards
9. Optics, botany, and the fibonacci numbers
10. Solving linear recurrence relations: the binet form for Fn
11. More on "" and "": Applications in trigonometry, physics, continued fractions, probability.
12. Examples from graph theory: An introduction to the lucas numbers
13. The lucas numbers: Further properties and examples
14. Matrices, the inverse tangent function, and an infinite sum
15. The ged property for the fibonacci numbers

Part two - The catalan numbers

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