Synopses & Reviews
This volume contains the proceedings of the Seventh International Research Conference on Fibonacci Numbers and their Applications. It includes a carefully refereed collection of papers dealing with number patterns, linear recurrences and the application of the Fibonacci Numbers to probability, statistics, differential equations, cryptography, computer science and elementary number theory. This volume provides a platform for recent discoveries and encourages further research. It is a continuation of the work presented in the previously published proceedings of the earlier conferences, and shows the growing interest in, and importance of, the pure and applied aspects of Fibonacci Numbers in many different areas of science. Audience: This book will be of interest to those whose work involves number theory, statistics and probability, algebra, numerical analysis, group theory and generalisations.
Table of Contents
Higher Order Bernoulli Polynomials and Newton Polygons; A. Adelberg. The Fibonacci Shuffle Tree; P.G. Anderson. On the Period of Sequences Modulo a Prime Satisfying a Second Order Recurrence; S. Ando. Generalizations to Large Hexagons of the Star of David Theorem with Respect to GCD; S. Ando, et al. Longest Success and Failure Runs and New Polynomials Related to the Fibonacci-Type Polynomials of Order K; D.L. Antzoulakos, A.N. Philippou. A Note on a Representation Conjecture by Hoggatt; M. Bicknell-Johnson. Some Remarks on the Distribution of Subsequences of Second Order Linear Recurrences; J.R. Burke. A Criterion for Stability of Two-Term Recurrence Sequences Modulo Odd Primes; W. Carlip, et al. A Problem of Diophantus and Pell Numbers; A. Dujella. On the Exceptional Set in the Problem of Diophantus and Davenport; A. Dujella. Substitutive Numeration Systems and a Combinatorial Problem; J.-M. Dumont. A Note on Derived Linear Recurring Sequences; M. Elia. Observations from Computer Experiments on an Integer Equation; D.C. Fielder, C.O. Alford. Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers; P. Filipponi, H.T. Freitag. First Derivative Sequences of Extended Fibonacci and Lucas Polynomials; P. Filipponi, A.F. Horadam. Elements of Zeckendorf Arithmetic; H.T. Freitag, G.M. Phillips. Binomial Coefficients Generalized with Respect to a Discrete Valuation; S. Frisch. The Dying Fibonacci Tree; B. Gittenberger. Smallest Integral Combinatorial Box; H. Harborth, M. Möller. New Aspects of Morgan-Voyce Polynomials; A.F. Horadam. Growing a Self-Similar Tree; Y. Horibe. Lacunary Sums of Binomial Coefficients; F.T. Howard, R. Witt. Some Reciprocal Summation Identities with Applications to the Fibonacci and Lucas Numbers; D. Jennings. A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients; C. Kimberling. On Sums of the Reciprocals of Prime Divisors of Terms of a Linear Recurrence; P. Kiss. A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal; W. Lang. A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature; T.N. Langtry. The Fibonacci Pyramid; T.G. Lavers. On a Three Dimensional Approximation Problem; K. Liptai. Analysis of the Euclidean and Related Algorithms; C.T. Long, W.A. Webb. Fundamental Solutions of u2-5v2 = -4r2; C.T. Long, W.A. Webb. Probable Prime Tests Using Lucas Sequences; W. More. On a Functional Equation Associated with the Fibonacci Numbers; K. Ozeki. Diophantine Properties of Linear Recursive Sequences I; A. Pethö. The Cantor-Fibonacci Distribution; H. Prodinger. On the Parity of Certain Partition Functions; N. Robbins. There are Infinitely Many Arithmetical Progressions Formed by Three Different Fibonacci Pseudoprimes; A. Rotkiewicz. On Mikolás' Summation Formula Involving Farey Fractions; K. Sato. Second Order Linear Recurring Sequences in Hypercomplex Numbers; K. Scheicher. The Bell Differential Polynomials; R. Schimming, S.Z. Rida. On Lucas d-Pseudoprimes; L. Somer. Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal Vs Immortal Trees; C.P. Spears, M. Bicknell-Johnson. The Golden Section and Modern Harmony Mathematics; A.P. Stakhov. Lucas Factors and a Fibonomial Generating Function; I. Strazdins. Elementary Properties of Canonical Number Systems in Quadratic Fields; J.M. Thuswaldner. Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences; R.F. Tichy. A Multivariate Inverse Polya Distribution of Order K Arising in the Case of Overlapping Success Runs; G.A. Tripsiannis, A.N. Philippou. Introduction to a Fibonacci Geometry; J.C. Turner, A.G. Shannon. Taylor Functionals and the Solution of Linear Difference Equations; L. Verde-Star. Section-Invariant Numbers and Generalised Golden Section Optimization Algorithms; A.A. Zhigljavsky, et al. Subject Index.