15 citations · 42 across the 5 of their papers we have counts for
5 papers
Legal Decompositions Arising from Non-positive Linear Recurrences
Minerva Catral, Pari L. Ford, Pamela E. Harris +2
Zeckendorf's theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers; this result has been generalized to many recurrence relati…
New Behavior in Legal Decompositions Arising from Non-positive Linear Recurrences
Minerva Catral, Pari L. Ford, Pamela E. Harris +4
Zeckendorf's theorem states every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. This result has been generalized to many sequences $\{a_n\…
Individual Gap Measures from Generalized Zeckendorf Decompositions
Robert Dorward, Pari L. Ford, Eva Fourakis +3
Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converge…
A Generalization of Zeckendorf's Theorem via Circumscribed -gons
Robert Dorward, Pari L. Ford, Eva Fourakis +4
Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers, where the Fibonacci numbers satisfy $F_n=F_{n-1}+F_…
Generalizing Zeckendorf's Theorem: The Kentucky Sequence
Minerva Catral, Pari Ford, Pamela Harris +2
By Zeckendorf's theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every posi…