Applications of fibonacci numbers : volume 8 : proceedings of 'The Eighth International Research Conference on Fibonacci Numbers and Their Applications', Rochester Institute of Technology, Rochester, New York, U.S.A., June 22-26, 1998

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. Cover......Page 1 Front matter......Page 2 1. On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences......Page 24 2. On Triangles and Squares Marked with Goldpoints—Studies of Golden Tiles......Page 34 3. Multivariate Pascal Polynomials of Order K with Probability Applications......Page 49 4. Fibonacci Planes and Spaces......Page 64 5. The Smallest Positive Integer Having F......Page 68 6. The Zeckendorf-Wythoff Array Applied to Counting the Number of Representations of N as Sums of Distinct Fibonacci Numbers......Page 74 7. Composing with Sequences: …But is It Art?......Page 82 8. Invariants for Linear Recurrences......Page 95 9. Base 10 RATS Cycles and Arbitrarily Long Base 10 RATS Cycles......Page 102 10. Quintics x......Page 113 11. The Pascal-De Moivre Moments and Their Generating Functions......Page 120 12. Investigating Special Binary Sequences with Some Computer Help......Page 138 13. Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials......Page 146 14. A Property of the Unit Digits of Recursive Sequences......Page 157 15. On General Divisibility of Sums of Integral Powers of the Golden Ratio......Page 165 16. Sylvester’s Algorithm and Fibonacci Numbers......Page 171 17. On the Characteristic Polynomial of the j-TH Order Fibonacci Sequence......Page 180 18. Quasi Morgan-Voyce Polynomials and Pell Convolutions......Page 193 19. On an Asymptotic Maximality of the Fibonacci Tree......Page 208 20. Generalizations of a Fibonacci Identity......Page 214 21. Some Generalizations of Wolstenholme’s Theorem......Page 225 22. Card Sorting Related to Fibonacci Numbers......Page 231 23. On the Inhomogeneous Geometric Line-Sequence......Page 244 24. Fibonacci Numbers of the Form k......Page 252 25. On Certain Polynomials of Even Subscripted Lucas Numbers......Page 261 26. On the Rank of Appearance of Lucas Sequences......Page 269 27. Algorithmic Simplification of Reciprocal Sums......Page 286 28. Solved and Unsolved Problems on Pseudoprime Numbers and Their Generalizations......Page 302 29. Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials......Page 316 30. Special Multipliers of Lucas Sequences Modulo p......Page 333 31. Digital Halftoning Using Error Diffusion and Linear Pixel Shuffling......Page 345 32. On Vector Sequence Recurrence Equations in Fibonacci Vector Geometry......Page 360 33. Constructing Identities Involving K......Page 376 Back matter......Page 387 This Volume Presents The Proceedings Of The Eighth International Conference On Fibonacci Numbers And Their Applications, Held In Rochester, New York, In June 1998. 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. Audience: 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. Edited By Fredric T. Howard. Proceedings of `The Eighth International Research Conference on Fibonacci Numbers and Their Applications', Rochester Institute of Technology, NY, USA