Applications of Fibonacci Numbers Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications

This book contains 28 research articles from among the 49 papers and abstracts presented at the Tenth International Conference on Fibonacci Numbers and Their Applications. These articles have been selected after a careful review by expert referees, and they range over many areas of mathematics. The Fibonacci numbers and recurrence relations are their unifying bond. We note that the article "Fibonacci, Vern and Dan" , which follows the Introduction to this volume, is not a research paper. It is a personal reminiscence by Marjorie Bicknell-Johnson, a longtime member of the Fibonacci Association. The editor believes it will be of interest to all readers. It is anticipated that this book, like the eight predecessors, will be useful to research workers and students at all levels who are interested in the Fibonacci numbers and their applications. March 16, 2003 The Editor Fredric T. Howard Mathematics Department Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Calvin Long, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv LIST OF CONTRlBUTORS TO THE CONFERENCE * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, ART, "Mathemagics.

Universal Bernoulli Polynomials and P-Adic Congruences.- A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties.- Fibinomial Identities.- Recounting Binomial Fibonacci Identities.- The Fibonacci Diatomic Array Applied to Fibonacci Representations.- On Purple Parrots, Fibonacci Numbers, and Color Theory.- Finding Fibonacci in a Fractal.- Positive Integers (a2 + b2)/(ab + 1) are Squares.- On the Fibonacci Length of Powers of Dihedral Groups.- Some Sums Related to Sums of Oresme Numbers.- Some Thoughts on Rook Polynomials on Square Chessboards.- Pythagorean Quadrilaterals.- A General Lacunary Recurrence Formula.- Ordering Words and Sets of Numbers: The Fibonacci Case.- Some Basic Properties of a Tribonacci Line-Sequence.- A Type of Sequence Constructed from Fibonacci Numbers.- Cullen Numbers in Binary Recurrent Sequences.- A Generalization of Euler’s Formula and its Connection to Fibonacci Numbers.- Extensions of Generalized Binomial Coefficients.- Some Parity Results Regarding t-Core Partitions.- Generalized Pell Numbers and Polynomials.- A Further Note on Lucasian Numbers.- Some Constructions and Theorems in Goldpoint Geometry.- Some Applications of Triangle Transformations in Fibonacci Geometry.- Cryptography and Lucas Sequence Discrete Logarithms.- Divisibility of an F-L Type Convolution.- Generating Functions of Convolution Matrices.- F-L Representation of Division of Polynomials over a Ring.