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Critical exponents of infinite balanced words

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1-s2.0-S0304397518306388-main.pdf (449.04 KB)

Date

2019-07-19

Authors

Rampersad, Narad
Shallit, Jeffrey
Vandomme, Élise

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + root2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + root5)/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.tcs.2018.10.017. © 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

infinite word, balanced word, Sturmian word, critical exponent

LC Keywords

Citation

URI

https://doi.org/10.1016/j.tcs.2018.10.017
 http://hdl.handle.net/10012/15702

Collections

Waterloo Research
Computer Science