Researcher ORCID Identifier
0009-0007-3839-7807
Graduation Year
2023
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Peter Kagey
Reader 2
Michael E. Orrison
Terms of Use & License Information
Rights Information
© 2023 Prakod Ngamlamai
Abstract
Integers are often represented as a base-$b$ representation by the sum $\sum c_ib^i$. Lekkerkerker and Zeckendorf later provided the rules for representing integers as the sum of Fibonacci numbers. Hannah Alpert then introduced the far-difference representation by providing rules for writing an integer with both positive and negative multiples of Fibonacci numbers. Our work aims to generalize her work to a broader family of linear recurrences. To do so, we describe desired properties of the representations, such as lexicographic ordering, and provide a family of algorithms for each linear recurrence that generate unique representations for any integer. We then prove other interesting properties of these representations such as summand-minimality.
Recommended Citation
Ngamlamai, Prakod, "Generalized Far-Difference Representations" (2023). HMC Senior Theses. 268.
https://scholarship.claremont.edu/hmc_theses/268
