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The number of valid factorizations of Fibonacci prefixes

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1-s2.0-S0304397518307497-main.pdf (416.95 KB)

Date

2019-07-05

Authors

Bonardo, Pierre
Frid, Anna E.
Shallit, Jeffrey

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

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.

Description

The 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/

Keywords

numeration systems, Fibonacci numeration system, Fibonacci word

LC Keywords

Citation

URI

https://doi.org/10.1016/j.tcs.2018.12.016
 http://hdl.handle.net/10012/15703

Collections

Waterloo Research
Computer Science