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. Front Matter....Pages i-xxxiii Universal Bernoulli Polynomials and P-Adic Congruences....Pages 1-8 A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties....Pages 9-18 Fibinomial Identities....Pages 19-24 Recounting Binomial Fibonacci Identities....Pages 25-28 The Fibonacci Diatomic Array Applied to Fibonacci Representations....Pages 29-38 On Purple Parrots, Fibonacci Numbers, and Color Theory....Pages 39-42 Finding Fibonacci in a Fractal....Pages 43-62 Positive Integers ( a 2 + b 2 )/( ab + 1) are Squares....Pages 63-67 On the Fibonacci Length of Powers of Dihedral Groups....Pages 69-85 Some Sums Related to Sums of Oresme Numbers....Pages 87-99 Some Thoughts on Rook Polynomials on Square Chessboards....Pages 101-108 Pythagorean Quadrilaterals....Pages 109-119 A General Lacunary Recurrence Formula....Pages 121-135 Ordering Words and Sets of Numbers: The Fibonacci Case....Pages 137-144 Some Basic Properties of a Tribonacci Line-Sequence....Pages 145-157 A Type of Sequence Constructed from Fibonacci Numbers....Pages 159-166 Cullen Numbers in Binary Recurrent Sequences....Pages 167-175 A Generalization of Euler’s Formula and its Connection to Fibonacci Numbers....Pages 177-185 Extensions of Generalized Binomial Coefficients....Pages 187-199 Some Parity Results Regarding t -Core Partitions....Pages 201-211 Generalized Pell Numbers and Polynomials....Pages 213-224 A Further Note on Lucasian Numbers....Pages 225-234 Some Constructions and Theorems in Goldpoint Geometry....Pages 235-245 Some Applications of Triangle Transformations in Fibonacci Geometry....Pages 247-261 Cryptography and Lucas Sequence Discrete Logarithms....Pages 263-266 Divisibility of an F-L Type Convolution....Pages 267-287 Generating Functions of Convolution Matrices....Pages 289-295 F-L Representation of Division of Polynomials over a Ring....Pages 297-308 Back Matter....Pages 309-311 This Volume Presents The Proceedings Of The Tenth International Conference On Fibonacci Numbers And Their Applications, Held In June 2002 In Flagstaff, Arizona. It Contains Research Papers On The Fibonacci Numbers And Their Generalizations. All Papers Were Carefully Refereed For Content And Originality. The Authors Represent Eight Different Countries. This Volume Will Be Of Interest To Graduate Students And Research Mathematicians, Whose Work Involves Number Theory, Combinatorics, Algebraic Number Theory, Finite Geometry And Special Functions. Edited By Frederic T. Howard. Proceedings of the Tenth International Research Conference on Fibonacci Numbers and Their Applications, held in Flagstaff, Arizona, USA, June 2002