Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xxviii

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2. Advances in Linear Pixel Shuffling

   • Peter G. Anderson

   Pages 1-21

3. Minimal Center Covering Stars with Respect to LCM in Pascal’s Pyramid and its Generalizations

   • Shiro Ando, Daihachiro Sato

   Pages 23-30

4. Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers

   • Shiro Ando, Daihachiro Sato

   Pages 31-45

5. Some Remarks on the Distribution of Second Order Recurrences and a Related Group Structure

   • John R. Burke

   Pages 47-52

6. Matrices, Recurrent Sequences and Arithmetic

   • Umberto Cerruti, Francesco Vaccarino

   Pages 53-62

7. Vector Linear Recurrence Sequences in Commutative Rings

   • Umberto Cerruti, Francesco Vaccarino

   Pages 63-72

8. Subwords of the Golden Sequence and the Fibonacci Words

   • Wai-fong Chuan

   Pages 73-84

9. Interesting Arrays Associated with Fibonacci Sequences

   • M. N. Deshpande, G. E. Bergum

   Pages 85-92

10. More Applications of a Partition Driven Symmetric Table

    • Daniel C. Fielder, Cecil O. Alford

    Pages 93-103

11. Partial Derivative Sequences of Second-Order Recurrence Polynomials

    • Piero Filipponi, Alwyn F. Horadam

    Pages 105-122

12. The Zeckendorf Decomposition of Certain Classes of Integers

    • Piero Filipponi, Herta T. Freitag

    Pages 123-135

13. On the Sum of Consecutive Squares

    • H. T. Freitag, G. M. Phillips

    Pages 137-142

14. Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz

    • Heiko Harborth, Silke Maasberg

    Pages 143-153

15. Rooks on Fibonacci Boards

    • Heiko Harborth, Lothar Piepmeyer

    Pages 155-163

16. Tiling with Cuisenaire Rods

    • E. O. Hare, P. Z. Chinn

    Pages 165-171

17. Hofstadter’s Conjecture for \(\alpha = \sqrt 2 - 1\)

    • Russell Jay Hendel

    Pages 173-199

18. Recursive Properties of Trigonometric Products

    • Russell Jay Hendel, Charles K. Cook

    Pages 201-214

19. A Synthesis of Certain Polynomial Sequences

    • A. F. Horadam

    Pages 215-229

20. Minmax Sequences for Pell Numbers

    • A. F. Horadam

    Pages 231-249

This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci Numbers and Their Applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. 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 five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 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 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

• Group theory
• LCM
• Number theory
• Prime
• cryptography
• finite field
• numerical analysis

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

  Gerald E. Bergum

• Aglangia, Nicosia, Cyprus

  Andreas N. Philippou

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

  Alwyn F. Horadam

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