Critical exponents of infinite balanced words
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Date
2019-07-19
Authors
Rampersad, Narad
Shallit, Jeffrey
Vandomme, Élise
Advisor
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