Applications of Fibonacci Numbers: Volume 3 Proceedings of ‘The Third International Conference on Fibonacci Numbers and Their Applications’, Pisa, Italy, July 25–29, 1988

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G.E. Bergum, Andreas Philippou, Alwyn F. Horadam
Springer Science & Business Media, Dec 31, 1989 - Mathematics - 366 pages
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This book contains thirty-six papers from among the forty-five papers presented at the Third International Conference on Fibonacci Numbers and Their Applications which was held in Pisa, Italy from July 25 to July 29, 1988 in honor of Leonardo de Pisa. 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 are their unifying bond. It is anticipated that this book, like its two predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. August 1989 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Andreas N. Philippou Ministry of Education Nicosia, Cyprus Alwyn F. Horadam University of New England Armidale N. S. W. , Australia xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Dvornicich, Roberto, Chairman Horadam, A. F. (Australia), Co-chairman Filipponi, Piero Philippou, A. N. (Cyprus), Co-chairman Perelli, Alberto Ando, S. (Japan) Viola, Carlo Bergum, G. E. (U. S. A. ) Zannier, Umberto Johnson, M. B. (U. S. A. ) Kiss, P. (Hungary) Tijdeman, Robert (The Netherlands) Tognetti, K. (Australia) XVII LIST OF CONTRIBUTORS TO THE CONFERENCE' ADLER, I. , RR 1, Box 532, North Bennington, VT 05257-9748. "Separating the Biological from the Mathematical Aspects of Phyllotaxis. " *AKRITAS, A. G. , (coauthor P. G. Bradford). "The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations.
 

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Contents

THE ROLE OF THE FIBONACCI SEQUENCE IN THE ISOLATION OF THE REAL ROOTS OF POLYNOMIAL EQUATIONS
1
A GCD PROPERTY ON PASCALS PYRAMID AND THE CORRESPONDING LCM PROPERTY OF THE MODIFIED PASCAL PYRAMID
7
TRANSLATABLE AND ROTATABLE CONFIGURATIONS WHICH GIVE EQUAL PRODUCT EQUAL GCD AND EQUAL LCM PROPERTIES S...
15
FIBONACCI LENGTH OF GENERATING PAIRS IN GROUPS
27
A GENERALIZATION OF FIBONACCI TREES
37
GENERALIZED FIBONACCI NUMBERS ARE ROUNDED POWERS
57
ON GENERALIZED FIBONACCI NUMBERS OF GRAPHS
63
AN INVESTIGATION OF SEQUENCES DERIVED FROM HOGGATT SUMS AND HOGGATT TRIANGLES
77
SOME RESULTS ON DIVISIBILITY SEQUENCES
181
ON MENTAL CALCULATION OF REPEATING DECIMALS FINDING FIBONACCI NUMBERS AND A CONNECTION TO PASCALS TRIANGLE
191
DIOPHANTINE REPRESENTATION OF FIBONACCI NUMBERS OVER NATURAL NUMBERS
197
ON PRIME DIVISORS OF THE TERMS OF SECOND ORDER LINEAR RECURRENCE SEQUENCES
203
AN ALTERNATING PRODUCT REPRESENTATION FOR REAL NUMBERS
209
MAXIMUM LENGTH OF THE EUCLIDEAN ALGORITHM AND CONTINUED FRACTIONS IN FX
217
RECURRENCE RELATIONS IN SINUSOIDS AND THEIR APPLICATIONS TO SPECTRAL ANALYSIS AND TO THE RESOLUTION OF ALGE...
223
A RECURRENCE RELATION FOR GAUSSIAN MULTINOMIAL COEFFICIENTS
239

AN APPLICATION TO MODERN CRYPTOGRAPHY
89
A NOTE ON RAMIFICATIONS CONCERNING THE CONSTRUCTION OF PYTHAGOREAN TRIPLES FROM RECURSIVE SEQUENCES
101
ON THE REPRESENTATION OF FknFn FknLn LknLn and LknFn as ZECKENDORF SUMS
107
FUNCTIONAL RECURRENCES
115
CONCENTRIC CYCLES IN MOSAIC GRAPHS
123
FIBONACCI TRIANGLES
129
MOSAIC NUMBERS OF FIBONACCI TREES
133
FALLING FACTORIAL POLYNOMIALS OF GENERALIZED FIBONACCI TYPE
139
SOME NOTES ON FIBONACCI BINARY SEQUENCES
155
CONGRUENCES FOR WEIGHTED AND DEGENERATE STIRLING NUMBERS
161
AN INVERSE THEOREM ON FIBONACCI NUMBERS
171
SOME BINOMIAL FIBONACCI IDENTITIES
241
A SURVEY OF PROPERTIES OF THIRD ORDER PELL DIAGONAL FUNCTIONS
255
MULTIVARIATE FIBONACCI POLYNOMIALS OF ORDER K AND THE MULTIPARAMETER NEGATIVE BINOMIAL DISTRIBUTION OF TH...
273
LONGEST CIRCULAR RUNS WITH AN APPLICATION IN RELIABILITY VIA THE FIBONACCITYPE POLYNOMIALS OF ORDER K
281
FIBONACCI NUMBERS AND AN ALGORITHM OF LEMOINE AND KÁTAI
287
GENERALIZATIONS OF SEQUENCES OF LUCAS AND BELL
299
DISTRIBUTION OF RESIDUES OF CERTAIN SECONDORDER LINEAR RECURRENCES MODULO P
311
THE FIBONACCI TREE HOFSTADTER AND THE GOLDEN STRING
325
THREE NUMBER TREES THEIR GROWTH RULES AND RELATED NUMBER PROPERTIES
335
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