Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xxiv

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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

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.

• LCM
• algorithms
• binomial
• boundary element method
• field
• matrix
• number theory
• polynomial
• prime number
• ring
• statistics

• 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

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