Bonardo, PierreFrid, Anna E.Shallit, Jeffrey2020-03-182020-03-182019-07-05https://doi.org/10.1016/j.tcs.2018.12.016http://hdl.handle.net/10012/15703The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.12.016. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalnumeration systemsFibonacci numeration systemFibonacci wordArticle