Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their ApplicationsAuthor: Frederic T. Howar Published by Springer Netherlands ISBN: 978-90-481-6545-2 DOI: 10.1007/978-0-306-48517-6Table of Contents: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 (a 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, 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, 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