Ebook: Applications of Fibonacci Numbers: Volume 5 Proceedings of ‘The Fifth International Conference on Fibonacci Numbers and Their Applications’, The University of St. Andrews, Scotland, July 20–July 24, 1992

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.

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Content:
Front Matter....Pages i-xxxiv
Multidimensional Golden Means....Pages 1-9
A Necessary and Sufficient Condition that Rays of a Star Configuration on Pascal’s Triangle Cover its Center with Respect to GCD and LCM....Pages 11-36
On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and its Generalizations....Pages 37-43
An Extension of an Old Classical Diophantine Problem....Pages 45-48
Fourier Analysis in Finite Nilpotent Groups....Pages 49-59
Wall and Vinson Revisited....Pages 61-68
Designer Decimals: Fractions which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left....Pages 69-75
Semigroup Presentations and Number Sequences....Pages 77-83
Counting the Number of Solutions of Congruences....Pages 85-101
On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials....Pages 103-112
Embedding Fibonacci Words into Fibonacci Word Patterns....Pages 113-122
On Sums of Cubes of Fibonacci Numbers....Pages 123-136
Integer Sided Triangles Whose Ratio of Altitude to Base is an Integer....Pages 137-142
On a Class of Iterative Recurrence Relations....Pages 143-158
Discrete Operational Calculi for Two-sided Sequences....Pages 159-168
Transformations of Fibonacci-Lucas Identities....Pages 169-184
Fibonacci Numbers and Continued Fraction Expansions....Pages 185-197
The DFF and DFFz Triangles and Their Mathematical Properties....Pages 199-206
Contributions from Cascaded Combinations to the Naming of Special Permutations....Pages 207-215
Fractal Patterns Derived from Rational Binomial Coefficients....Pages 217-219
Hausdorff Dimension in Pascal’s Triangle....Pages 221-228
Chaos, Elliptic Curves and All That....Pages 229-244
Co-Related Sequences Satisfying the General Second Order Recurrence Relation....Pages 245-256
On the Moments of the Sum-of-Digits Function....Pages 257-262
Problems on Fibonacci and B-Adic Tree Representations by Regular K-Gons....Pages 263-271
Two-Distance Sets and the Golden Ratio....Pages 273-277
A Fibonacci Problem Classification Scheme Useful to Undergraduate Pedagogy....Pages 279-288
Zeckendorf Representations of Positive and Negative Integers by Pell Numbers....Pages 289-304
Integration Sequences of Fibonacci and Lucas Polynomials....Pages 305-316
Pell-Type Number Generators of Pythagorean Triples....Pages 317-330
Balance Morphology of a Binary Tree....Pages 331-343
On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials....Pages 345-354
A Sequence Arising from Reflections in Multiple Glass Plates....Pages 355-366
Diophantine Representation of Non-Fibonacci Numbers....Pages 367-377
On Some Problems Related to the Fibonacci Group....Pages 379-386
Orderings of the Set of All Positive Fibonacci Sequences....Pages 387-392
Some Results Concerning the Reciprocal Sum of Prime Divisors of a Lucas Number....Pages 393-397
Rational Numbers with Predictable Engel Product Expansions....Pages 399-403
Two Families of Orthogonal Polynomial Systems Related to Fibonacci Chains....Pages 405-416
On the Formation of Higher Order Higher Dimensional Line-Sequential Vector Spaces....Pages 417-420
Arithmetic Sequences and Second order Recurrences....Pages 421-427
Generalized Fibonacci Pseudoprimes and Probable Primes....Pages 429-440
A Generalization of the Fibonacci Sequence....Pages 441-447
How to Advance on a Stairway by Coin Flippings....Pages 449-457
Fibonacci Sequence and its Generalizations Hidden in Algorithms for Generating Morse Codes....Pages 459-464
On Matrix Representations of Generalized Fibonacci Numbers and Their Applications....Pages 465-472
A Cholesky Decomposition in Matching Insulin Profiles....Pages 473-479
Generalized Exponential and Trigonometric Functions....Pages 481-486
Divisibility of Terms in Lucas Sequences by Their Subscripts....Pages 487-496
Upper Bounds for Frequencies of Elements in Second-Order Recurrences over A Finite Field....Pages 497-506
On the Convergence of Quotients of Some Recursive Sequences....Pages 507-514
Two Distribution Problems for Polynomials....Pages 515-525
The Elements of Enteger Geometry....Pages 527-546
Totient Functions on the Euler Number Tree....Pages 547-560
Using Matrix Techniques to Establish Properties of k-Order Linear Recursive Sequences....Pages 561-568
Back Matter....Pages 569-583
....Pages 585-600