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Publications (2)

math.CO2014

The Distribution of Gaps between Summands in Generalized Zeckendorf Decompositions

Amanda Bower, Rachel Insoft, Shiyu Li +2

Zeckendorf proved that any integer can be decomposed uniquely as a sum of non-adjacent Fibonacci numbers, $F_{n}$ . Using continued fractions, Lekkerkerker proved the average number o…

math.NT2012

The Average Gap Distribution for Generalized Zeckendorf Decompositions

Olivia Beckwith, Amanda Bower, Louis Gaudet +4

An interesting characterization of the Fibonacci numbers is that, if we write them as $F_{1} = 1$ , $F_{2} = 2$ , $F_{3} = 3$ , $F_{4} = 5, ...$ , then every positive integer can be written un…