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Low complexity binary words avoiding (5/2)+-powers.

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Title: Low complexity binary words avoiding (5/2)+-powers.
Authors: Currie, James1, Rampersad, Narad1
Source: Discrete Mathematics & Theoretical Computer Science (DMTCS). 2025, Vol. 27 Issue 3, p1-12. 12p.
Subjects: Binary sequences, Combinatorics, Scholars
Abstract: Rote words are infinite words that contain 2n factors of length n for every n ≥ 1. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid (5/2)+-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid (5/2)+-powers, confirming a conjecture of Ollinger and Shallit. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Low complexity binary words avoiding (5/2)<superscript>+</superscript>-powers.
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  Data: <searchLink fieldCode="DE" term="%22Binary+sequences%22">Binary sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Scholars%22">Scholars</searchLink>
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  Data: Rote words are infinite words that contain 2n factors of length n for every n ≥ 1. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid (5/2)+-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid (5/2)+-powers, confirming a conjecture of Ollinger and Shallit. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: 2025
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