Researcher ORCID Identifier
Graduation Year
2021
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Arthur T. Benjamin
Reader 2
Francis E. Su
Terms of Use & License Information
Rights Information
2021 John R Lentfer
Abstract
Zeckendorf’s theorem states that every positive integer can be decomposed uniquely into a sum of non-consecutive Fibonacci numbers (where f1 = 1 and f2 = 2). Previous work by Grabner and Tichy (1990) and Miller and Wang (2012) has found a generalization of Zeckendorf’s theorem to a larger class of recurrent sequences, called Positive Linear Recurrence Sequences (PLRS’s). We apply well-known tiling interpretations of recurrence sequences from Benjamin and Quinn (2003) to PLRS’s. We exploit that tiling interpretation to create a new tiling interpretation specific to PLRS’s that captures the behavior of the generalized Zeckendorf’s theorem.
Recommended Citation
Lentfer, John, "Tiling Representations of Zeckendorf Decompositions" (2021). HMC Senior Theses. 247.
https://scholarship.claremont.edu/hmc_theses/247
