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Applications of Fibonacci Numbers

Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers and Their Applications’, Wake Forest University, N.C., U.S.A., July 30–August 3, 1990

  • Conference proceedings
  • © 1991

Overview

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. University of New England, Armidale, Australia

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Table of contents (33 papers)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. A Fibonacci-Based Pseudo-Random Number Generator

    • Peter G. Anderson
    Pages 1-8

  3. On the Proof of GCD and LCM Equalities Concerning the Generalized Binomial and Multinomial Coefficients

    • Shiro Ando, Daihachiro Sato
    Pages 9-16

  4. Supercube

    • Joseph Arkin, David C. Arney, Lee S. Dewald, Frank R. Giordano
    Pages 17-32

  5. A Note on Fundamental Properties of Recurring Series

    • Joseph Arkin, David C. Arney, Frank R. Giordano, Rickey A. Kolb
    Pages 33-36

  6. Period Patterns of Certain Second-Order Linear Recurrences Modulo a Prime

    • David Banks, Lawrence Somer
    Pages 37-40

  7. Nearly Isosceles Triangles Where the Vertex Angle is a Multiple of the Base Angle

    • Marjorie Bicknell-Johnson
    Pages 41-50

  8. The Ring of Fibonacci (Fibonacci “Numbers” with Matrix Subscript)

    • Odoardo Brugia, Piero Filipponi, Francesco Mazzarella
    Pages 51-62

  9. One-Relator Products of Cyclic Groups and Fibonacci-Like Sequences

    • C. M. Campbell, P. M. Heggie, E. F. Robertson, R. M. Thomas
    Pages 63-68

  10. A Generalization of the Fibonacci Search

    • Renato M. Capocelli
    Pages 69-76

  11. Pascal’s Triangle: Top Gun or Just One of the Gang?

    • Daniel C. Fielder, Cecil O. Alford
    Pages 77-90

  12. Conversion of Fibonacci Identities into Hyperbolic Identities Valid for an Arbitrary Argument

    • Piero Filipponi, Herta T. Freitag
    Pages 91-98

  13. Derivative Sequences of Fibonacci and Lucas Polynomials

    • Piero Filipponi, Alwyn F. Horadam
    Pages 99-108

  14. A Carry Theorem for Rational Binomial Coefficients

    • Dan Flath, Rhodes Peele
    Pages 109-120

  15. On Co-Related Sequences Involving Generalized Fibonacci Numbers

    • H. T. Freitag, G. M. Phillips
    Pages 121-125

  16. Fibonacci and B-Adic Trees in Mosaic Graphs

    • Heiko Harborth, Sabine Jäger
    Pages 127-132

  17. Fibonacci Representations of Graphs

    • Heiko Harborth, Arnfried Kemnitz
    Pages 133-138

  18. On the Sizes of Elements in the Complement of a Submonoid of Integers

    • Chung-wu Ho, James L. Parish, Jau-shyong Shiue
    Pages 139-144

  19. Genocchi Polynomials

    • A. F. Horadam
    Pages 145-166

  20. An Application of Zeckendorf’s Theorem

    • Roger V. Jean
    Pages 167-170
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Keywords

About this book

This book contains thirty-three papers from among the thirty-eight papers presented at the Fourth International Conference on Fibonacci Numbers and Their Applications which was held at Wake Forest University, Winston-Salem, North Carolina from July 30 to August 3, 1990. 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 three predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. March 1, 1991 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Alwyn F. Horadam University of New England Armidale, N. S. W. , Australia Andreas N. Philippou Minister of Education Ministry of Education Nicosia, Cyprus xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Howard, Fred T. , Co-Chair Horadam, A. F. (Australia), Co-Chair Waddill, Marcellus E. , Co-Chair Philippou, A. N. (Cyprus), Co-Chair Hayashi, Elmer K. Ando, S. (Japan) Bergum, G. E. (U. S. A. ) Vaughan, Theresa Harrell, Deborah Bicknell-Johnson, M. B. (U. S. A. ) Campbell, Colin (Scotland) Filipponi, Piero (Italy) Kiss, P. (Hungary) Turner, J. C. (New Zealand) xvii LIST OF CONTRIBUTORS TO THE CONFERENCE *ALFORD, CECIL 0. , (coauthor Daniel C. Fielder) "Pascal's Triangle: Top Gun or Just One of the Gang?" *ANDERSON, PETER G. , "A Fibonacci-Based Pseudo-Random Number Generator.

Editors and Affiliations

  • South Dakota State University, Brookings, USA

    G. E. Bergum

  • Ministry of Education, Nicosia, Cyprus

    A. N. Philippou

  • University of New England, Armidale, Australia

    A. F. Horadam

Bibliographic Information

  • Book Title: Applications of Fibonacci Numbers

  • Book Subtitle: Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers and Their Applications’, Wake Forest University, N.C., U.S.A., July 30–August 3, 1990

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

  • DOI: https://doi.org/10.1007/978-94-011-3586-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1991

  • Hardcover ISBN: 978-0-7923-1309-0Published: 30 June 1991

  • Softcover ISBN: 978-94-010-5590-1Published: 30 October 2012

  • eBook ISBN: 978-94-011-3586-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XXIV, 313

  • Topics: Number Theory, Algebra, Statistics, general, Computational Mathematics and Numerical Analysis

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