Patrick Dynes

most citedGaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

10 citations · 11 across the 4 of their papers we have counts for

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math.NT2015★ 1 cited

Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . Previo…

math.NT2014

Benford Behavior of Generalized Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by $F_{1} = 1, F_{2} = 2$ and $F_{n + 1} = F_{n} + F_{n - 1}$ , every…

math.NT2014★ 10 cited

Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . We con…

math.NT2014

Benford Behavior of Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers ${F_{i}}_{i = 1}^{\infty}$ . A set $S \subset \…