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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

  • Conference proceedings
  • © 1990

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Editors:
  1. G. E. Bergum

    1. South Dakota State University, Brookings, USA

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  2. A. N. Philippou

    1. Ministry of Education, Nicosia, Cyprus

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  3. A. F. Horadam

    1. Department of Math., Stat., & Comp. Sci., University of New England, Armidale, Australia

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Table of contents (36 papers)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations

    • A. G. Akritas, P. G. Bradford
    Pages 1-6

  3. A GCD Property on Pascal’s Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid

    • Shiro Ando, Daihachiro Sato
    Pages 7-14

  4. Translatable and Rotatable Configurations which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously

    • Shiro Ando, Daihachiro Sato
    Pages 15-26

  5. Fibonacci Length of Generating Pairs in Groups

    • C. M. Campbell, H. Doostie, E. F. Robertson
    Pages 27-35

  6. A Generalization of Fibonacci Trees

    • Renato M. Capocelli
    Pages 37-56

  7. Generalized Fibonacci Numbers are Rounded Powers

    • Renato M. Capocelli, Paul Cull
    Pages 57-62

  8. On Generalized Fibonacci Numbers of Graphs

    • Michael Drmota
    Pages 63-76

  9. An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles

    • Daniel C. Fielder, Cecil O. Alford
    Pages 77-88

  10. Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography

    • Piero Filipponi, Emilio Montolivo
    Pages 89-99

  11. A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences

    • Herta T. Freitag
    Pages 101-106

  12. On the Representation of {F kn /F n }, {F kn /L n }, {L kn /L n }, and {L kn /F n } as Zeckendorf Sums

    • Herta T. Freitag
    Pages 107-114

  13. Functional Recurrences

    • Krystyna Grytczuk, Aleksander Grytczuk
    Pages 115-121

  14. Concentric Cycles in Mosaic Graphs

    • Heiko Harborth
    Pages 123-128

  15. Fibonacci Triangles

    • Heiko Harborth, Arnfried Kemnitz
    Pages 129-132

  16. Mosaic Numbers of Fibonacci Trees

    • Heiko Harborth, Sabine Lohmann
    Pages 133-138

  17. Falling Factorial Polynomials of Generalized Fibonacci Type

    • A. F. Horadam
    Pages 139-153

  18. Some Notes on Fibonacci Binary Sequences

    • Yasuichi Horibe
    Pages 155-160

  19. Congruences for Weighted and Degenerate Stirling Numbers

    • F. T. Howard
    Pages 161-170

  20. An Inverse Theorem on Fibonacci Numbers

    • Naotaka Imada
    Pages 171-179
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Keywords

About this book

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.

Editors and Affiliations

  • South Dakota State University, Brookings, USA

    G. E. Bergum

  • Ministry of Education, Nicosia, Cyprus

    A. N. Philippou

  • Department of Math., Stat., & Comp. Sci., University of New England, Armidale, Australia

    A. F. Horadam

Bibliographic Information

  • Book Title: Applications of Fibonacci Numbers

  • Book Subtitle: Volume 3 Proceedings of ‘The Third International Conference on Fibonacci Numbers and Their Applications’, Pisa, Italy, July 25–29, 1988

  • Editors: G. E. Bergum, A. N. Philippou, A. F. Horadam

  • DOI: https://doi.org/10.1007/978-94-009-1910-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1990

  • Hardcover ISBN: 978-0-7923-0523-1Published: 31 December 1989

  • Softcover ISBN: 978-94-010-7352-3Published: 03 October 2013

  • eBook ISBN: 978-94-009-1910-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XXIV, 366

  • Topics: Number Theory, Statistics, general, Computational Mathematics and Numerical Analysis, Sequences, Series, Summability

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