Monochromatic arithmetic progressions in the Fibonacci, Thue–Morse, and Rudin–Shapiro words.
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| Title: | Monochromatic arithmetic progressions in the Fibonacci, Thue–Morse, and Rudin–Shapiro words. |
|---|---|
| Authors: | Joshi, G.1 (AUTHOR) gandhar.joshi@open.ac.uk, Rust, D.1 (AUTHOR) dan.rust@open.ac.uk |
| Source: | Theoretical Computer Science. Sep2025, Vol. 1050, pN.PAG-N.PAG. 1p. |
| Subjects: | Arithmetic series, Dynamical systems, Number systems, Walnut, Rotational motion |
| Abstract: | We investigate the lengths and starting positions of the longest monochromatic arithmetic progressions for a fixed difference in the Fibonacci word. We provide a complete classification for their lengths in terms of a simple formula. Our strongest results are proved using methods from dynamical systems, especially the dynamics of circle rotations. We also employ computer-based methods in the form of the automatic theorem-proving software Walnut. This allows us to extend recent results concerning similar questions for the Thue–Morse word and the Rudin–Shapiro word. This also allows us to obtain some results for the Fibonacci word that do not seem to be amenable to dynamical methods. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 186629306 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Monochromatic arithmetic progressions in the Fibonacci, Thue–Morse, and Rudin–Shapiro words. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Joshi%2C+G%2E%22">Joshi, G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gandhar.joshi@open.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Rust%2C+D%2E%22">Rust, D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dan.rust@open.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Sep2025, Vol. 1050, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Arithmetic+series%22">Arithmetic series</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Number+systems%22">Number systems</searchLink><br /><searchLink fieldCode="DE" term="%22Walnut%22">Walnut</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion%22">Rotational motion</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We investigate the lengths and starting positions of the longest monochromatic arithmetic progressions for a fixed difference in the Fibonacci word. We provide a complete classification for their lengths in terms of a simple formula. Our strongest results are proved using methods from dynamical systems, especially the dynamics of circle rotations. We also employ computer-based methods in the form of the automatic theorem-proving software Walnut. This allows us to extend recent results concerning similar questions for the Thue–Morse word and the Rudin–Shapiro word. This also allows us to obtain some results for the Fibonacci word that do not seem to be amenable to dynamical methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=186629306 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.tcs.2025.115391 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Arithmetic series Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: Number systems Type: general – SubjectFull: Walnut Type: general – SubjectFull: Rotational motion Type: general Titles: – TitleFull: Monochromatic arithmetic progressions in the Fibonacci, Thue–Morse, and Rudin–Shapiro words. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Joshi, G. – PersonEntity: Name: NameFull: Rust, D. IsPartOfRelationships: – BibEntity: Dates: – D: 27 M: 09 Text: Sep2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 03043975 Numbering: – Type: volume Value: 1050 Titles: – TitleFull: Theoretical Computer Science Type: main |
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