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# Applications of Fibonacci Numbers : Volume 3 Proceedings of `The Third International Conference on Fibonacci Numbers and Their Applications', Pisa, Italy, July 25-29, 1988

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## Description

This book contains thirty-six papers from among the forty-five papers presented at the Third International Conference on Fibonacci Numbers and Their Applications which was held in Pisa, Italy from July 25 to July 29, 1988 in honor of Leonardo de Pisa. 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 are their unifying bond. It is anticipated that this book, like its two predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. August 1989 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Andreas N. Philippou Ministry of Education Nicosia, Cyprus Alwyn F. Horadam University of New England Armidale N. S. W. , Australia xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Dvornicich, Roberto, Chairman Horadam, A. F. (Australia), Co-chairman Filipponi, Piero Philippou, A. N. (Cyprus), Co-chairman Perelli, Alberto Ando, S. (Japan) Viola, Carlo Bergum, G. E. (U. S. A. ) Zannier, Umberto Johnson, M. B. (U. S. A. ) Kiss, P. (Hungary) Tijdeman, Robert (The Netherlands) Tognetti, K. (Australia) XVII LIST OF CONTRIBUTORS TO THE CONFERENCE' ADLER, I. , RR 1, Box 532, North Bennington, VT 05257-9748. "Separating the Biological from the Mathematical Aspects of Phyllotaxis. " *AKRITAS, A. G. , (coauthor P. G. Bradford). "The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations.

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## Product details

- Hardback | 366 pages
- 156 x 233.9 x 23.6mm | 730.3g
- 01 Jan 1990
- Springer
- Dordrecht, Netherlands
- English
- 1990 ed.
- XXIV, 366 p.
- 079230523X
- 9780792305231

## Table of contents

The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations.- A GCD Property on Pascal's Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid.- Translatable and Rotatable Configurations Which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously.- Fibonacci Length of Generating Pairs in Groups.- A Generalization of Fibonacci Trees.- Generalized Fibonacci Numbers are Rounded Powers.- On Generalized Fibonacci Numbers of Graphs.- An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles.- Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography.- A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences.- On the Representation of {Fkn/Fn}, {Fkn/Ln

}, {Lkn/Ln} and {Lkn/Fn} as Zeckendorf Sums.- Functional Recurrences.- Concentric Cycles in Mosaic Graphs.- Fibonacci Triangles.- Mosaic Numbers of Fibonacci Trees.- Falling Factorial Polynomials of Generalized Fibonacci Type.- Some Notes on Fibonacci Binary Sequences.- Congruences for Weighted and Degenerate Stirling Numbers.- An Inverse Theorem on Fibonacci Numbers.- Some Results on Divisibility Sequences.- On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal's Triangle.- Diophantine Representation of Fibonacci Numbers Over Natural Numbers.- On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences.- An Alternating Product Representation for Real Numbers.- Maximum Length of the Euclidean Algorithm and Continued Fractions in F(X).- Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations.- A Recurrence Relation for Gaussian Multinomial Coefficients.- Some Binomial Fibonacci Identities.- A Survey of Properties of Third Order Pell Diagonal Functions.- Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order.- Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K.- Fibonacci Numbers and an Algorithm of Lemoine and Katai.- Generalizations of Sequences of Lucas and Bell.- Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P.- The Fibonacci Tree, Hofstadter and the Golden String.- Three Number Trees - Their Growth Rules and Related Number Properties.

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}, {Lkn/Ln} and {Lkn/Fn} as Zeckendorf Sums.- Functional Recurrences.- Concentric Cycles in Mosaic Graphs.- Fibonacci Triangles.- Mosaic Numbers of Fibonacci Trees.- Falling Factorial Polynomials of Generalized Fibonacci Type.- Some Notes on Fibonacci Binary Sequences.- Congruences for Weighted and Degenerate Stirling Numbers.- An Inverse Theorem on Fibonacci Numbers.- Some Results on Divisibility Sequences.- On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal's Triangle.- Diophantine Representation of Fibonacci Numbers Over Natural Numbers.- On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences.- An Alternating Product Representation for Real Numbers.- Maximum Length of the Euclidean Algorithm and Continued Fractions in F(X).- Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations.- A Recurrence Relation for Gaussian Multinomial Coefficients.- Some Binomial Fibonacci Identities.- A Survey of Properties of Third Order Pell Diagonal Functions.- Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order.- Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K.- Fibonacci Numbers and an Algorithm of Lemoine and Katai.- Generalizations of Sequences of Lucas and Bell.- Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P.- The Fibonacci Tree, Hofstadter and the Golden String.- Three Number Trees - Their Growth Rules and Related Number Properties.

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