Honors College Theses
Publication Date
2024
Major
Mathematics (M.S.)
Release Option
Open Access
Faculty Mentor
Sungkon Chang
Abstract
Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon Chang. This thesis focuses on similar results for third order Fibonacci sequences where the uniqueness clause is not satisfied.
Copyright
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Recommended Citation
Aguilar, Samuel A., "Zeckendorf Representation Analysis on Third Order Fibonacci Sequences that Do Not Satisfy the Uniqueness Property" (2024). Honors College Theses. 1003.
https://digitalcommons.georgiasouthern.edu/honors-theses/1003
