Fibonacci and Lucas Numbers with Applications

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshevpolynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians.

As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition;conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities toexplore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration.

In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity.

Volume II features:

• A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication.
• Numerous combinatorial and graph-theoretic proofs and techniques.
• A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them.
• Examples of the beauty, power, and ubiquity of the extended gibonacci family.
• An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models.
• Abbreviated solutions provided for all odd-numbered exercises.
• Extensive references for further study.

This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.

Keywords:

Fibonacci and Lucas Polynomials; Pascal’s Triangle; Ends of The Numbers Ln; Generating Functions; Pell and Pell-Lucas Polynomials; Composition of Lucas Polynomials; De Moivre-Like Formulas; Fibonacci-Lucas Bridges; Applications of Identity; Infinite Products; Putnam Delight Revisited; Infinite Simple Continued Fraction; Q-Matrix; Summation Formulas; A Recurrence for Fn2; Divisibility Properties; A Model for Fibonacci Polynomials; A Ladder Model; A Model for Pell-Lucas Polynomials; Coloured Tilings; A New Tiling Scheme; A Model for Pell-Lucas Polynomials; A Domino Model for Fibonacci Polynomials; Another Model for Fibonacci Polynomials; Graph-Theoretic Models II; Q-Matrix and Connected Graph;Weighted Paths; Q-Matrix Revisited; Byproducts of The Model; A Bijection Algorithm; Fibonacci and Lucas Sums; Fibonacci Walks