Elsevier

Theoretical Computer Science

Volume 775, 5 July 2019, Pages 68-75
Theoretical Computer Science

The number of valid factorizations of Fibonacci prefixes

https://doi.org/10.1016/j.tcs.2018.12.016Get rights and content
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Abstract

We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci words. In particular, we show that the sequence V(n) is the shuffle of the ceilings of two linear functions of n.

Keywords

Numeration systems
Fibonacci numeration system
Fibonacci word

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