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S-adic characterization of minimal dendric shifts.

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Title: S-adic characterization of minimal dendric shifts.
Authors: Gheeraert, France1, Leroy, Julien2
Source: Discrete Mathematics & Theoretical Computer Science (DMTCS). 2025, Vol. 27 Issue 2, p1-36. 36p.
Subjects: Free groups, Families, Vocabulary, Language & languages, Automorphisms
Abstract: Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive S-adic representation where the morphisms in S are positive tame automorphisms of the free group generated by the alphabet. In this paper, we present an S-adic characterization of this family using two finite graphs. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric. [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: Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive S-adic representation where the morphisms in S are positive tame automorphisms of the free group generated by the alphabet. In this paper, we present an S-adic characterization of this family using two finite graphs. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric. [ABSTRACT FROM AUTHOR]
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  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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      – Code: eng
        Text: English
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              Text: 2025
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