The Dynamics of the Fibonacci Partition Function

Abstract: The Fibonacci partition function $R(n)$ counts the number of ways of representing a natural number $n$ as the sum of distinct Fibonacci numbers. For example, $R(6)=2$ since $6=5+1$ and $6=3+2+1$. An explicit formula for $R(n)$ was recently given by Chow and Slattery. In this talk we express $R(n)$ in terms of ergodic sums over an irrational rotation, which allows us to prove lots of statements about the local structure of $R(n)$.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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