The number of valid factorizations of Fibonacci prefixes
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Date
2019-07-05
Authors
Bonardo, Pierre
Frid, Anna E.
Shallit, Jeffrey
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
We establish several recurrence relations and an explicit formula for , 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 is the shuffle of the ceilings of two linear functions of n.
Description
The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.12.016 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
numeration systems, fibonacci numeration system, fibonacci word