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Volume 58 Number 5
(Special Open Access Issue)
December 2020

Proceedings

of the 19th International Conference
on Fibonacci Numbers and Their Applications

Online Conference
July 21 - 23, 2020


Editors-in-Chief: Steven J. Miller and Lejla Smajlović
Editors: Thomas Martinez, Zenan Šabanac, and Lamija Šćeta


CONTENTS

Marjorie Bicknell-Johnson
Conference Report
1
     Full text

Santiago Alzate, Oscar Correa, and Rigoberto Flórez
Fibonacci Identities from Jordan Identities
2
     Abstract | Full text

Peter G. Anderson
The Fibonacci Word as a 2-adic Number and its Continued Fraction
21
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Bob Bastasz
Lyndon Words of a Second-Order Recurrence
25
     Abstract | Full text

Arthur T. Benjamin, John Lentfer, and Thomas C. Martinez
Counting on Euler and Bernoulli Number Identities
30
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Matthew Blair, Rigoberto Flórez, Antara Mukherjee, and José L. Ramírez
Matrices in the Determinant Hosoya Triangle
34
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Elżbieta Bołdyriew, Anna Cusenza, Linglong Dai, Pei Ding, Aidan Dunkelberg, John Haviland, Kate Huffman, Dianhui Ke, Daniel Kleber, Jason kuretski, John Lentfer, Tianhao Luo, Steven J. Miller, Clayton Mizgerd, Vashisth Tiwari, Jingkai Ye, Yunhao Zhang, Xiaoyan Zheng, and Weiduo Zhu
Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation
55
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Elżbieta Bołdyriew, John Haviland, Phúc Lâm, John Lentfer, Steven J. Miller, and Fernando Trejos Suárez
An Introduction to Completeness of Positive Linear Recurrence Sequences
77
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Bruce M. Boman
Geometric Capitulum Patterns Based on Fibonacci p-Proportions
91
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Zakariae Bouazzaoui
On Periods of Fibonacci Sequences and Real Quadratic p-rational Fields
103
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Spiros D. Dafnis
On the Relation Between Fibonacci and Lucas Numbers
111
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Daniel Duverney and Yohei Tachiya
Linear Independence of Infinite Products Generated by the Lucas Numbers
115
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Kenneth Edwards and Michael A. Allen
A New Combinatorial Interpretation of the Fibonacci Numbers Cubed
128
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Russell Jay Hendel
Recursive Triangles Appearing Embedded in Recursive Families
135
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Burghard Herrmann
The Continued Fraction Pendulum
144
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Ruoci Li, Xiaonan Li, Steven J. Miller, Clayton Mizgerd, Chenyang Sun, Dong Xia, and Zhyi Zhou
Deterministic Zeckendorf Games
152
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Augustine O. Munagi
An Identity for Inverse-Conjugate Compositions
161
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Kouichi Nakagawa
A Triangle with Sides Lengths of a Rational Power of the Plastic Constant
166
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Sam Northshield
Topographs; Conway and Otherwise
172
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R. L. Ollerton and A. G. Shannon
A Note on Brousseau's Summation Problem
190
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Genki Shibukawa
New Identities for Some Symmetric Polynomials, and a Higher Order Analogue of the Fibonacci and Lucas Numbers
200
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Anitha Srinivasan
The Markoff-Fibonacci Numbers
222
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Kai Wang
Girard-Waring Type Formula for a Generalized Fibonacci Sequence
229
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Steven J. Miller (Editor)
Problem Section
236
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