Applications of Fibonacci Numbers

This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its seven predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 1, 1999 The Editor F. T. Howard Mathematics and Computer Science Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC USA xvii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Anderson, Peter G. , Chairman Horadam, A. F. (Australia), Co-Chair Arpaya, Pasqual Philippou, A. N. (Cyprus), Co-Chair Biles, John Bergum, G. E. (U. S. A. ) Orr, Richard Filipponi, P. (Italy) Radziszowski, Stanislaw Harborth, H. (Germany) Rich, Nelson Horibe, Y. (Japan) Howard, F. (U. S. A. ) Johnson, M. (U. S. A. ) Kiss, P. (Hungary) Phillips, G. M. (Scotland) Turner, J. (New Zealand) Waddill, M. E. (U. S. A. ) xix LIST OF CONTRIBUTORS TO THE CONFERENCE AGRATINI, OCTAVIAN, "Unusual Equations in Study. " ANDO, SHIRO, (coauthor Daihachiro Sato), "On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences. " ANATASSOVA, VASSIA K. , (coauthor J. C.

Klappentext

This volume presents the Proceedings of the Eighth International Conference on Fibonacci Numbers and their Applications, held in Rochester, New York, in June 1998. br/ All papers have been carefully refereed for content and originality and represent a continuation of the work of previous conferences. This book, describing recent discoveries and encouraging future research, shows the growing interest in and the importance of the pure and applied aspects of Fibonacci Numbers in many different areas of science. br/ emAudience/em: This volume will be of interest to graduate students and research mathematicians whose work involves number theory, combinatorics, algebraic number theory, field theory and polynomials, finite geometry and special functions.

Inhalt
On The Generalized Binomial Coefficients Defined by Strong Divisibility Sequences.- On Triangles and Squares Marked with GoldpointsStudies of Golden Tiles.- Multivariate Pascal Polynomials of Order K with Probability Applications.- Fibonacci Planes and Spaces.- The Smallest Positive Integer Having Fk Representations as Sums of Distinct Fibonacci Numbers.- The Zeckendorf-Wythoff Array Applied to Counting the Number of Representations of N as Sums of Distinct Fibonacci Numbers.- Composing With Sequences: But is It Art?.- Invariants for Linear Recurrences.- Base 10 RATS Cycles and Arbitrarily Long Base 10 RATS Cycles.- Quintics x5 - 5x - k, the Golden Section, and Square Lucas Numbers.- The Pascal-De Moivre Moments and Their Generating Functions.- Investigating Special Binary Sequences with Some Computer Help.- Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials.- A Property of the Unit Digits of Recursive Sequences.- On General Divisibility of Sums of Integral Powers of the Golden Ratio.- Sylvester's Algorithm and Fibonacci Numbers.- On the Characteristic Polynomial of the J-th Order Fibonacci Sequence.- Quasi Morgan-Voyce Polynomials and Pell Convolutions.- On an Asymptotic Maximality of the Fibonacci Tree.- Generalizations of a Fibonacci Identity.- Some Generalizations of Wolstenholme's Theorem.- Card Sorting Related to Fibonacci Numbers.- On the Inhomogeneous Geometric Line-Sequence.- Fibonacci Numbers of the Form k2 + k + 2.- On Certain Polynomials of Even Subscripted Lucas Numbers.- On the Rank of Appearance of Lucas Sequences.- Algorithmic Simplification of Reciprocal Sums.- Solved and Unsolved Problems on Pseudoprime Numbers and Their Generalizations.- Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials.- SpecialMultipliers of Lucas Sequences Modulo pr.- Digital Halftoning Using Error Diffusion and Linear Pixel Shuffling.- On Vector Sequence Recurrence Equations in Fibonacci Vector Geometry.- Constructing Identities Involving Kth-Order F-L Numbers by Using the Characteristic Polynomial.