The dynamics of the Fibonacci partition function
Tom Kempton (Manchester)
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). This talk should be accessible to all, no knowledge of dynamics or number theory will be assumed.
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