15 citations · 34 across the 6 of their papers we have counts for
6 papers
Bin Decompositions
Daniel Gotshall, Pamela E. Harris, Dawn Nelson +2
It is well known that every positive integer can be expressed as a sum of nonconsecutive Fibonacci numbers provided the Fibonacci numbers satisfy for $n\geq…
On the Asymptotic Behavior of Variance of PLRS Decompositions
Steven J. Miller, Dawn Nelson, Zhao Pan +1
A positive linear recurrence sequence is of the form with each and , with appropriately chosen initial conditi…
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\…
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…
A Variation on Leopoldt's Conjecture: Some Local Units instead of All Local Units
Dawn C. Nelson
Leopoldt's Conjecture is a statement about the relationship between the global and local units of a number field. Approximately the conjecture states that the Z_p-rank of the diago…