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arXiv · 1806.09534

The number of valid factorizations of Fibonacci prefixes

Pierre Bonardo·Anna E. Frid·Jeffrey Shallit
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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.

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Pierre Bonardo, Anna E. Frid, Jeffrey Shallit. 2019-01-07. The number of valid factorizations of Fibonacci prefixes. https://doi.org/10.1016/j.tcs.2018.12.016

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