Applications of Fibonacci Numbers de G.E. Bergum

Applications of Fibonacci Numbers: Volume 7

G.E. Bergum

Andreas N. Philippou

Alwyn F. Horadam

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.

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Express

Paperback (6)

379^.88 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 oct 2012

379^.88 lei 6-8 săpt.

SPRINGER NETHERLANDS – 20 sep 2011

393^.16 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 dec 2010

619^.34 lei 6-8 săpt.

SPRINGER NETHERLANDS – 3 oct 2013

626^.81 lei 6-8 săpt.

SPRINGER NETHERLANDS – 13 oct 2012

632^.87 lei 6-8 săpt.

SPRINGER NETHERLANDS – 21 oct 2012

639^.52 lei 6-8 săpt.

Hardback (4)

626^.36 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 apr 1988

626^.36 lei 6-8 săpt.

SPRINGER NETHERLANDS – 31 dec 1989

632^.99 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 apr 1998

639^.06 lei 6-8 săpt.

SPRINGER NETHERLANDS – 30 sep 1993

646^.35 lei 6-8 săpt.

Cuprins

Higher Order Bernoulli Polynomials and Newton Polygons.- The Fibonacci Shuffle Tree.- On The Period of Sequences Modulo a Prime Satisfying a Second Order Recurrence.- Generalizations to Large Hexagons of The Star of David Theorem With Respect to God.- Longest Success and Failure Runs and New Polynomials Related to The Fibonacci-Type Polynomials of Order K.- A Note on A Representation Conjecture By Hoggatt.- Some Remarks on The Distribution of Subsequences of Second Order Linear Recurrences.- A Criterion for Stability of Two-Term Recurrence Sequences Modulo Odd Primes.- A Problem of Diophantus and Pell Numbers.- On The Exceptional Set in The Problem of Diophantus and Davenport.- Substitutive Numeration Systems and A Combinatorial Problem.- A Note on Derived Linear Recurring Sequences.- Observations from Computer Experiments on an Integer Equation.- Some Probabilistic Aspects of The Zeckendorf Decomposition of Integers.- First Derivative Sequences of Extended Fibonacci and Lucas Polynomials.- Elements of Zeckendorf Arithmetic.- Binomial Coefficients Generalized With Respect to A Discrete Valuation.- The Dying Fibonacci Tree.- Smallest Integral Combinatorial Box.- New Aspects of Morgan-Voyce Polynomials.- Growing A Self-Similar Tree.- Lacunary Sums of Binomial Coefficients.- Some Reciprocal Summation Identities with Applications to The Fibonacci And Lucas Numbers.- A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients.- On Sums of The Reciprocals of Prime Divisors of Terms of a Linear Recurrence.- A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal.- A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature.- The Fibonacci Pyramid.- On A Three Dimensional Approximation Problem.- Analysis of The Euclidean and Related Algorithms.- Fundamental Solutions of u2 — 5v2 = — 4r2.- Probable Prime Tests Using Lucas Sequences.- On a Functional Equation Associated with The Fibonacci Numbers.- Diophantine Properties of Linear Recursive Sequences I.- The Cantor-Fibonacci Distribution.- On The Parity of Certain Partition Functions.- There Are Infinitely Many Arithmetical Progressions Formed By Three Different Fibonacci Pseudoprimes.- On Mikolas’ Summation Formula Involving Farey Fractions.- Second order Linear Recurring Sequences in Hypercomplex Numbers.- The Bell Differential Polynomials.- On Lucas d-Pseudoprimes.- Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal Vs Immortal Trees.- The Golden Section and Modern Harmony Mathematics.- Lucas Factors and A Fibonomial Generating Function.- Elementary Properties of Canonical Number Systems in Quadratic Fields.- Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences.- A Multivariate Inverse Polya Distribution Of Order K Arising in the Case Of Overlapping Success Runs.- to A Fibonacci Geometry.- Taylor Functionals and The Solution of Linear Difference Equations.- Section — Invariant Numbers and Generalised Golden Section Optimization Algorithms.