#15242 - $\mathcal{S}$-adic characterization of minimal dendric shifts

<!DOCTYPE html><html xmlns="http://www.w3.org/1999/xhtml"> <head prefix="og: https://ogp.me/ns# article: http://ogp.me/ns/article# profile: http://ogp.me/ns/profile#"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" > <meta name="citation_journal_title" content="Discrete Mathematics & Theoretical Computer Science" > <meta name="citation_author" content="France Gheeraert" > <meta name="citation_author" content="Julien Leroy" > <meta name="citation_title" content="$\mathcal{S}$-adic characterization of minimal dendric shifts" > <meta name="citation_publication_date" content="2025-02-14" > <meta name="citation_volume" content="vol. 27:2" > <meta name="citation_issue" content="Combinatorics" > <meta name="citation_doi" content="10.46298/dmtcs.13130" > <meta name="citation_fulltext_world_readable" content="" > <meta name="citation_pdf_url" content="https://dmtcs.episciences.org/15242/pdf" > <meta name="citation_issn" content="1365-8050" > <meta name="citation_arxiv_id" content="2206.00333" > <meta name="citation_language" content="" > <meta name="citation_article_type" content="Research Article" > <meta name="citation_keywords" content="Mathematics - Dynamical Systems" > <meta name="citation_keywords" content="Computer Science - Discrete Mathematics" > <meta name="citation_keywords" content="68R15, 37B10" > <meta name="DC.creator" content="France Gheeraert" > <meta name="DC.creator" content="Julien Leroy" > <meta name="DC.language" content="" > <meta name="DC.title" content="$\mathcal{S}$-adic characterization of minimal dendric shifts" > <meta name="DC.type" content="journal" > <meta name="DC.identifier" content="15242" > <meta name="DC.identifier" content="https://dmtcs.episciences.org/15242" > <meta name="DC.identifier" content="https://dmtcs.episciences.org/15242/pdf" > <meta name="DC.identifier" content="10.46298/dmtcs.13130" > <meta name="DC.description" content="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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of 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." > <meta name="DC.subject" content="Mathematics - Dynamical Systems" > <meta name="DC.subject" content="Computer Science - Discrete Mathematics" > <meta name="DC.subject" content="68R15, 37B10" > <meta name="DC.date" content="2025-02-14" > <meta name="DC.relation.ispartof" content="Discrete Mathematics & Theoretical Computer Science" > <meta name="DC.citation.volume" content="vol. 27:2" > <meta name="DC.publisher" content="Episciences.org" > <meta property="og:title" content="$\mathcal{S}$-adic characterization of minimal dendric shifts" > <meta property="og:type" content="article" > <meta property="og:article:published_time" content="2025-02-14 16:02:17" > <meta property="og:article:modified_time" content="2025-03-27 17:51:11" > <meta property="og:article:author" content="France Gheeraert" > <meta property="og:article:author" content="Julien Leroy" > <meta property="og:article:tag" content="Mathematics - Dynamical Systems" > <meta property="og:article:tag" content="Computer Science - Discrete Mathematics" > <meta property="og:article:tag" content="68R15, 37B10" > <meta property="og:url" content="https://dmtcs.episciences.org/15242" > <meta property="og:image" content="https://dmtcs.episciences.org/img/episciences_logo_1081x1081.jpg" > <meta property="og:description" content="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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of 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." > <meta property="og:site_name" content="Episciences" > <meta name="twitter:card" content="summary_large_image" > <meta name="twitter:site" content="@episciences" > <meta name="twitter:title" content="$\mathcal{S}$-adic characterization of minimal dendric shifts" > <meta name="twitter:description" content="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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of 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." > <meta name="twitter:image" content="https://dmtcs.episciences.org/img/episciences_logo_1081x1081.jpg" > <meta name="twitter:image:alt" content="Episciences Logo" > <meta name="description" content="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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of two finite graphs. 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collapsable" style="margin-top: 20px"><div class="panel-heading"><h2 class="panel-title" style="margin-bottom: 5px"><span class="darkgrey">France Gheeraert ; Julien Leroy - </span>$\mathcal{S}$-adic characterization of minimal dendric shifts</h2>dmtcs:13130 - Discrete Mathematics & Theoretical Computer Science, February 14, 2025, vol. 27:2 - <a rel="noopener" target="_blank" href="https://doi.org/10.46298/dmtcs.13130"> https://doi.org/10.46298/dmtcs.13130</a></div><div class="panel-body in"><strong>$\mathcal{S}$-adic characterization of minimal dendric shifts</strong><span class="label label-default pull-right">Article</span><p><i><div id="paper-authors">Authors: France Gheeraert ; Julien Leroy </div><div id="orcid-author-existing" class="hidden">NULL##NULL</div><div id="authors-list" class="hidden">France Gheeraert;Julien Leroy</div></i></p><ul class="list-unstyled"></ul><p class="small force-word-wrap" style=""> 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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of 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. </p><hr></hr><div class="paper-doi small"><a rel="noopener" target="_blank" href="https://doi.org/10.46298/dmtcs.13130"> https://doi.org/10.46298/dmtcs.13130</a></div><div class="small">Source: <a target="_blank" href="https://arxiv.org/abs/2206.00333v4">arXiv.org:2206.00333</a></div><div class="small">Volume: vol. 27:2</div><div class="small">Section: Combinatorics</div><div class="small">Published on: February 14, 2025</div><div class="small">Accepted on: January 10, 2025</div><div class="small">Submitted on: February 27, 2024</div><div class="small force-word-wrap">Keywords: Mathematics - Dynamical Systems,Computer Science - Discrete Mathematics,68R15, 37B10</div><div class="small">Licence: <a rel="noopener" target="_blank" href="https://creativecommons.org/licenses/by/4.0">Attribution 4.0 International (CC BY 4.0)</a></div><div id="record-loading" 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#15242 - $\mathcal{S}$-adic characterization of minimal dendric shifts