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On a sequence of Kimberling and its relationship to the Tribonacci word.

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Title: On a sequence of Kimberling and its relationship to the Tribonacci word.
Authors: Dvořáková, Lubomíra1, Pelantová, Edita1, Shallit, Jeffrey2
Source: Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-14. 14p.
Subjects: Binary sequences, Critical exponents, Mathematics
Abstract: In 2017, Clark Kimberling defined an interesting sequence B = 0100101100 of 0's and 1's by certain inflation rules, and he made a number of conjectures about this sequence and some related ones. In this note we prove his conjectures using, in part, the Walnut theorem-prover. We show how his word is related to the infinite Tribonacci word, and we determine both the factor complexity and critical exponent of B. [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.)
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  Data: On a sequence of Kimberling and its relationship to the Tribonacci word.
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  Data: <searchLink fieldCode="AR" term="%22Dvořáková%2C+Lubomíra%22">Dvořáková, Lubomíra</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Pelantová%2C+Edita%22">Pelantová, Edita</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Shallit%2C+Jeffrey%22">Shallit, Jeffrey</searchLink><relatesTo>2</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Mathematics+%26+Theoretical+Computer+Science+%28DMTCS%29%22">Discrete Mathematics & Theoretical Computer Science (DMTCS)</searchLink>. 2026, Vol. 28 Issue 2, p1-14. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Binary+sequences%22">Binary sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Critical+exponents%22">Critical exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
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  Data: In 2017, Clark Kimberling defined an interesting sequence B = 0100101100 of 0's and 1's by certain inflation rules, and he made a number of conjectures about this sequence and some related ones. In this note we prove his conjectures using, in part, the Walnut theorem-prover. We show how his word is related to the infinite Tribonacci word, and we determine both the factor complexity and critical exponent of B. [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: 2026
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