Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xxxiv

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2. Multidimensional Golden Means

   • Peter G. Anderson

   Pages 1-9

3. A Necessary and Sufficient Condition that Rays of a Star Configuration on Pascal’s Triangle Cover its Center with Respect to GCD and LCM

   • Shiro Ando, Daihachiro Sato

   Pages 11-36

4. On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and its Generalizations

   • Shiro Ando, Daihachiro Sato

   Pages 37-43

5. An Extension of an Old Classical Diophantine Problem

   • Joseph Arkin, David C. Arney, Frank R. Giordano, Rickey A. Kolb, Gerald E. Bergum

   Pages 45-48

6. Fourier Analysis in Finite Nilpotent Groups

   • Huseyin Aydin, Geoff C. Smith

   Pages 49-59

7. Wall and Vinson Revisited

   • Huseyin Aydin, Ramazan Dikici, Geoff C. Smith

   Pages 61-68

8. Designer Decimals: Fractions which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left

   • Marjorie Bicknell-Johnson

   Pages 69-75

9. Semigroup Presentations and Number Sequences

   • Colin M. Campbell, Edmund F. Robertson, Richard M. Thomas

   Pages 77-83

10. Counting the Number of Solutions of Congruences

    • Umberto Cerruti

    Pages 85-101

11. On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials

    • O. Chryssaphinou, S. Papastavridis, T. Tsapelas

    Pages 103-112

12. Embedding Fibonacci Words into Fibonacci Word Patterns

    • Wai-fong Chuan

    Pages 113-122

13. On Sums of Cubes of Fibonacci Numbers

    • Stuart Clary, Paul D. Hemenway

    Pages 123-136

14. Integer Sided Triangles Whose Ratio of Altitude to Base is an Integer

    • Charles K. Cook, Gerald E. Bergum

    Pages 137-142

15. On a Class of Iterative Recurrence Relations

    • Karl Dilcher

    Pages 143-158

16. Discrete Operational Calculi for Two-sided Sequences

    • Ivan H. Dimovski, Virginia S. Kiryakova

    Pages 159-168

17. Transformations of Fibonacci-Lucas Identities

    • L. A. G. Dresel

    Pages 169-184

18. Fibonacci Numbers and Continued Fraction Expansions

    • Michael Drmota

    Pages 185-197

19. The DFF and DFFz Triangles and Their Mathematical Properties

    • Marco Faccio, Giuseppe Ferri, Arnaldo D’Amico

    Pages 199-206

20. Contributions from Cascaded Combinations to the Naming of Special Permutations

    • Daniel C. Fielder, Cecil O. Alford

    Pages 207-215

This book contains 58 papers from among the 68 papers presented at the Fifth International Conference on Fibonacci Numbers and Their Applications which was held at the University of St. Andrews, St. Andrews, Fife, Scotland from July 20 to July 24, 1992. 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 four predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 5, 1993 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 Government House Z50 Nicosia, Cyprus xxv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Campbell, Colin M., Co-Chair Horadam, A.F. (Australia), Co-Chair Phillips, George M., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Foster, Dorothy M.E. Ando, S. (Japan) McCabe, John H. Bergum, G.E. (U.S.A.) Filipponi, P. (Italy) O'Connor, John J.

• LCM
• Permutation
• Prime
• Vector space
• binomial
• calculus
• classification
• continued fraction
• cryptography
• finite field
• number theory
• numerical analysis
• statistics

• Computer Science Department, South Dakota State University, Brookings, USA

  Gerald E. Bergum

• Ministry of Education, Nicosia, Cyprus

  Andreas N. Philippou

• Department of Mathematics, Statistics and Computer Science, University of New England, Armidale, Australia

  Alwyn F. Horadam

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