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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Leroy, J"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.12534">arXiv:2410.12534</a> <span> [<a href="https://arxiv.org/pdf/2410.12534">pdf</a>, <a href="https://arxiv.org/ps/2410.12534">ps</a>, <a href="https://arxiv.org/format/2410.12534">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</span> </div> </div> <p class="title is-5 mathjax"> Stability properties for subgroups generated by return words </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gheeraert%2C+F">France Gheeraert</a>, <a href="/search/cs?searchtype=author&query=Goulet-Ouellet%2C+H">Herman Goulet-Ouellet</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Stas%2C+P">Pierre Stas</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.12534v1-abstract-short" style="display: inline;"> Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stab… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.12534v1-abstract-full').style.display = 'inline'; document.getElementById('2410.12534v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.12534v1-abstract-full" style="display: none;"> Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stability for subgroups generated by return words. Within this framework, we revisit several existing results and generalize some of them. We also study general aspects of stability, such as decidability or closure under certain operations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.12534v1-abstract-full').style.display = 'none'; document.getElementById('2410.12534v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37B10 (Primary) 68R15 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.15075">arXiv:2406.15075</a> <span> [<a href="https://arxiv.org/pdf/2406.15075">pdf</a>, <a href="https://arxiv.org/ps/2406.15075">ps</a>, <a href="https://arxiv.org/format/2406.15075">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</span> </div> </div> <p class="title is-5 mathjax"> Algebraic characterization of dendricity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gheeraert%2C+F">France Gheeraert</a>, <a href="/search/cs?searchtype=author&query=Goulet-Ouellet%2C+H">Herman Goulet-Ouellet</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Stas%2C+P">Pierre Stas</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.15075v1-abstract-short" style="display: inline;"> Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.15075v1-abstract-full').style.display = 'inline'; document.getElementById('2406.15075v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.15075v1-abstract-full" style="display: none;"> Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every set of return words is a basis of the free group over the alphabet. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.15075v1-abstract-full').style.display = 'none'; document.getElementById('2406.15075v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.00333">arXiv:2206.00333</a> <span> [<a href="https://arxiv.org/pdf/2206.00333">pdf</a>, <a href="https://arxiv.org/ps/2206.00333">ps</a>, <a href="https://arxiv.org/format/2206.00333">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.46298/dmtcs.13130">10.46298/dmtcs.13130 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> $\mathcal{S}$-adic characterization of minimal dendric shifts </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gheeraert%2C+F">France Gheeraert</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.00333v4-abstract-short" style="display: inline;"> 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… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.00333v4-abstract-full').style.display = 'inline'; document.getElementById('2206.00333v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.00333v4-abstract-full" style="display: none;"> 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. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.00333v4-abstract-full').style.display = 'none'; document.getElementById('2206.00333v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">36 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15; 37B10 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Discrete Mathematics & Theoretical Computer Science, vol. 27:2, Combinatorics (February 14, 2025) dmtcs:13130 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.10092">arXiv:2102.10092</a> <span> [<a href="https://arxiv.org/pdf/2102.10092">pdf</a>, <a href="https://arxiv.org/ps/2102.10092">ps</a>, <a href="https://arxiv.org/format/2102.10092">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> </div> <p class="title is-5 mathjax"> $\mathcal{S}$-adic characterization of minimal ternary dendric shifts </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Gheeraert%2C+F">France Gheeraert</a>, <a href="/search/cs?searchtype=author&query=Lejeune%2C+M">Marie Lejeune</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.10092v2-abstract-short" style="display: inline;"> 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… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.10092v2-abstract-full').style.display = 'inline'; document.getElementById('2102.10092v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.10092v2-abstract-full" style="display: none;"> 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 investigate those $\mathcal{S}$-adic representations, heading towards an $\mathcal{S}$-adic characterization of this family. We obtain such a characterization in the ternary case, involving a directed graph with 2 vertices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.10092v2-abstract-full').style.display = 'none'; document.getElementById('2102.10092v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15; 37B10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.11698">arXiv:1911.11698</a> <span> [<a href="https://arxiv.org/pdf/1911.11698">pdf</a>, <a href="https://arxiv.org/format/1911.11698">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Information Retrieval">cs.IR</span> </div> </div> <p class="title is-5 mathjax"> Doc2Vec on the PubMed corpus: study of a new approach to generate related articles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Dynomant%2C+E">Emeric Dynomant</a>, <a href="/search/cs?searchtype=author&query=Darmoni%2C+S+J">St茅fan J. Darmoni</a>, <a href="/search/cs?searchtype=author&query=Lejeune%2C+%C3%89">脡meline Lejeune</a>, <a href="/search/cs?searchtype=author&query=Kerdelhu%C3%A9%2C+G">Ga毛tan Kerdelhu茅</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Jean-Philippe Leroy</a>, <a href="/search/cs?searchtype=author&query=Lequertier%2C+V">Vincent Lequertier</a>, <a href="/search/cs?searchtype=author&query=Canu%2C+S">St茅phane Canu</a>, <a href="/search/cs?searchtype=author&query=Grosjean%2C+J">Julien Grosjean</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.11698v1-abstract-short" style="display: inline;"> PubMed is the biggest and most used bibliographic database worldwide, hosting more than 26M biomedical publications. One of its useful features is the "similar articles" section, allowing the end-user to find scientific articles linked to the consulted document in term of context. The aim of this study is to analyze whether it is possible to replace the statistic model PubMed Related Articles (pmr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11698v1-abstract-full').style.display = 'inline'; document.getElementById('1911.11698v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.11698v1-abstract-full" style="display: none;"> PubMed is the biggest and most used bibliographic database worldwide, hosting more than 26M biomedical publications. One of its useful features is the "similar articles" section, allowing the end-user to find scientific articles linked to the consulted document in term of context. The aim of this study is to analyze whether it is possible to replace the statistic model PubMed Related Articles (pmra) with a document embedding method. Doc2Vec algorithm was used to train models allowing to vectorize documents. Six of its parameters were optimised by following a grid-search strategy to train more than 1,900 models. Parameters combination leading to the best accuracy was used to train models on abstracts from the PubMed database. Four evaluations tasks were defined to determine what does or does not influence the proximity between documents for both Doc2Vec and pmra. The two different Doc2Vec architectures have different abilities to link documents about a common context. The terminological indexing, words and stems contents of linked documents are highly similar between pmra and Doc2Vec PV-DBOW architecture. These algorithms are also more likely to bring closer documents having a similar size. In contrary, the manual evaluation shows much better results for the pmra algorithm. While the pmra algorithm links documents by explicitly using terminological indexing in its formula, Doc2Vec does not need a prior indexing. It can infer relations between documents sharing a similar indexing, without any knowledge about them, particularly regarding the PV-DBOW architecture. In contrary, the human evaluation, without any clear agreement between evaluators, implies future studies to better understand this difference between PV-DBOW and pmra algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.11698v1-abstract-full').style.display = 'none'; document.getElementById('1911.11698v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> H.3.3; I.2.7 <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> H.3.3; I.2.7 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.07330">arXiv:1812.07330</a> <span> [<a href="https://arxiv.org/pdf/1812.07330">pdf</a>, <a href="https://arxiv.org/ps/1812.07330">ps</a>, <a href="https://arxiv.org/format/1812.07330">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Computing the $k$-binomial complexity of the Thue--Morse word </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Lejeune%2C+M">Marie Lejeune</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.07330v1-abstract-short" style="display: inline;"> Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.07330v1-abstract-full').style.display = 'inline'; document.getElementById('1812.07330v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.07330v1-abstract-full" style="display: none;"> Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the set of factors of length $n$ occurring in $\mathbf{x}$. This complexity measure has not been investigated very much. In this paper, we characterize the $k$-binomial complexity of the Thue--Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue--Morse word is aperiodic, its $k$-binomial complexity eventually takes only two values. In this paper, we first obtain general results about the number of occurrences of subwords appearing in iterates of the form $唯^\ell(w)$ for an arbitrary morphism $唯$. We also thoroughly describe the factors of the Thue--Morse word by introducing a relevant new equivalence relation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.07330v1-abstract-full').style.display = 'none'; document.getElementById('1812.07330v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1806.04891">arXiv:1806.04891</a> <span> [<a href="https://arxiv.org/pdf/1806.04891">pdf</a>, <a href="https://arxiv.org/format/1806.04891">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> </div> <p class="title is-5 mathjax"> Decidability of the isomorphism and the factorization between minimal substitution subshifts </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Durand%2C+F">Fabien Durand</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1806.04891v3-abstract-short" style="display: inline;"> Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic, but the existing invariants are not sufficient for this purpose. We first show that given two minimal substitution subshifts, there exists a computable constant… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.04891v3-abstract-full').style.display = 'inline'; document.getElementById('1806.04891v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1806.04891v3-abstract-full" style="display: none;"> Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic, but the existing invariants are not sufficient for this purpose. We first show that given two minimal substitution subshifts, there exists a computable constant $R$ such that any factor map between these subshifts (if any) is the composition of a factor map with a radius smaller than $R$ and some power of the shift map. Then we prove that it is decidable to check whether a given sliding block code is a factor map between two prescribed minimal substitution subshifts. As a consequence of these two results, we provide an algorithm that, given two minimal substitution subshifts, decides whether one is a factor of the other and, as a straightforward corollary, whether they are isomorphic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.04891v3-abstract-full').style.display = 'none'; document.getElementById('1806.04891v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">65 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37B10; 68R15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1801.06349">arXiv:1801.06349</a> <span> [<a href="https://arxiv.org/pdf/1801.06349">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Human-Computer Interaction">cs.HC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> Proceedings of eNTERFACE 2015 Workshop on Intelligent Interfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Mancas%2C+M">Matei Mancas</a>, <a href="/search/cs?searchtype=author&query=Frisson%2C+C">Christian Frisson</a>, <a href="/search/cs?searchtype=author&query=Tilmanne%2C+J">Jo毛lle Tilmanne</a>, <a href="/search/cs?searchtype=author&query=d%27Alessandro%2C+N">Nicolas d'Alessandro</a>, <a href="/search/cs?searchtype=author&query=Barborka%2C+P">Petr Barborka</a>, <a href="/search/cs?searchtype=author&query=Bayansar%2C+F">Furkan Bayansar</a>, <a href="/search/cs?searchtype=author&query=Bernard%2C+F">Francisco Bernard</a>, <a href="/search/cs?searchtype=author&query=Fiebrink%2C+R">Rebecca Fiebrink</a>, <a href="/search/cs?searchtype=author&query=Heloir%2C+A">Alexis Heloir</a>, <a href="/search/cs?searchtype=author&query=Hemery%2C+E">Edgar Hemery</a>, <a href="/search/cs?searchtype=author&query=Laraba%2C+S">Sohaib Laraba</a>, <a href="/search/cs?searchtype=author&query=Moinet%2C+A">Alexis Moinet</a>, <a href="/search/cs?searchtype=author&query=Nunnari%2C+F">Fabrizio Nunnari</a>, <a href="/search/cs?searchtype=author&query=Ravet%2C+T">Thierry Ravet</a>, <a href="/search/cs?searchtype=author&query=Reboursi%C3%A8re%2C+L">Lo茂c Reboursi猫re</a>, <a href="/search/cs?searchtype=author&query=Sarasua%2C+A">Alvaro Sarasua</a>, <a href="/search/cs?searchtype=author&query=Tits%2C+M">Micka毛l Tits</a>, <a href="/search/cs?searchtype=author&query=Tits%2C+N">No茅 Tits</a>, <a href="/search/cs?searchtype=author&query=Zaj%C3%A9ga%2C+F">Fran莽ois Zaj茅ga</a>, <a href="/search/cs?searchtype=author&query=Alborno%2C+P">Paolo Alborno</a>, <a href="/search/cs?searchtype=author&query=Kolykhalova%2C+K">Ksenia Kolykhalova</a>, <a href="/search/cs?searchtype=author&query=Frid%2C+E">Emma Frid</a>, <a href="/search/cs?searchtype=author&query=Malafronte%2C+D">Damiano Malafronte</a>, <a href="/search/cs?searchtype=author&query=Veld%2C+L+H+i">Lisanne Huis in't Veld</a>, <a href="/search/cs?searchtype=author&query=Cakmak%2C+H">H眉seyin Cakmak</a> , et al. (49 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1801.06349v1-abstract-short" style="display: inline;"> The 11th Summer Workshop on Multimodal Interfaces eNTERFACE 2015 was hosted by the Numediart Institute of Creative Technologies of the University of Mons from August 10th to September 2015. During the four weeks, students and researchers from all over the world came together in the Numediart Institute of the University of Mons to work on eight selected projects structured around intelligent interf… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1801.06349v1-abstract-full').style.display = 'inline'; document.getElementById('1801.06349v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1801.06349v1-abstract-full" style="display: none;"> The 11th Summer Workshop on Multimodal Interfaces eNTERFACE 2015 was hosted by the Numediart Institute of Creative Technologies of the University of Mons from August 10th to September 2015. During the four weeks, students and researchers from all over the world came together in the Numediart Institute of the University of Mons to work on eight selected projects structured around intelligent interfaces. Eight projects were selected and their reports are shown here. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1801.06349v1-abstract-full').style.display = 'none'; document.getElementById('1801.06349v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">159 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.10065">arXiv:1705.10065</a> <span> [<a href="https://arxiv.org/pdf/1705.10065">pdf</a>, <a href="https://arxiv.org/format/1705.10065">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> </div> <p class="title is-5 mathjax"> Counting Subwords Occurrences in Base-b Expansions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a>, <a href="/search/cs?searchtype=author&query=Stipulanti%2C+M">Manon Stipulanti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.10065v1-abstract-short" style="display: inline;"> We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence $(S_b(n))_{n\ge 0}$ counting the number of positive entries on each row of a generalization of the Pascal triangle to binomial coefficients of base-$b$ expansions. By using a convenient tree structure, we provide recurrence relations for… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.10065v1-abstract-full').style.display = 'inline'; document.getElementById('1705.10065v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.10065v1-abstract-full" style="display: none;"> We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence $(S_b(n))_{n\ge 0}$ counting the number of positive entries on each row of a generalization of the Pascal triangle to binomial coefficients of base-$b$ expansions. By using a convenient tree structure, we provide recurrence relations for $(S_b(n))_{n\ge 0}$ leading to the $b$-regularity of the latter sequence. Then we deduce the asymptotics of the summatory function of the sequence $(S_b(n))_{n\ge 0}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.10065v1-abstract-full').style.display = 'none'; document.getElementById('1705.10065v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11A63; 11B65; 11B85; 41A60; 68R15 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Integers 18A (2018), no. A13, 32 pp </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.08343">arXiv:1705.08343</a> <span> [<a href="https://arxiv.org/pdf/1705.08343">pdf</a>, <a href="https://arxiv.org/format/1705.08343">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.disc.2017.01.003">10.1016/j.disc.2017.01.003 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Counting the number of non-zero coefficients in rows of generalized Pascal triangles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a>, <a href="/search/cs?searchtype=author&query=Stipulanti%2C+M">Manon Stipulanti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.08343v1-abstract-short" style="display: inline;"> This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$ counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for $(S(n))_{n\ge 0}$. This lea… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08343v1-abstract-full').style.display = 'inline'; document.getElementById('1705.08343v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.08343v1-abstract-full" style="display: none;"> This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence $(S(n))_{n\ge 0}$ counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for $(S(n))_{n\ge 0}$. This leads to a connection with the $2$-regular Stern-Brocot sequence and the sequence of denominators occurring in the Farey tree. Then we extend our construction to the Zeckendorf numeration system based on the Fibonacci sequence. Again our tree structure permits us to obtain recurrence relations for and the F-regularity of the corresponding sequence. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08343v1-abstract-full').style.display = 'none'; document.getElementById('1705.08343v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Discrete Math. 340 (2017) 862-881 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.08322">arXiv:1705.08322</a> <span> [<a href="https://arxiv.org/pdf/1705.08322">pdf</a>, <a href="https://arxiv.org/format/1705.08322">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Behavior of digital sequences through exotic numeration systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a>, <a href="/search/cs?searchtype=author&query=Stipulanti%2C+M">Manon Stipulanti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.08322v1-abstract-short" style="display: inline;"> Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of gene… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08322v1-abstract-full').style.display = 'inline'; document.getElementById('1705.08322v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.08322v1-abstract-full" style="display: none;"> Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of generalized Pascal triangles and binomial coefficients of words. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08322v1-abstract-full').style.display = 'none'; document.getElementById('1705.08322v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">32 pages, 27 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11A63; 11B85; 41A60 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Electron. J. Combin. 24 (2017), no. 1, Paper 1.44, 36 pp </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.08270">arXiv:1705.08270</a> <span> [<a href="https://arxiv.org/pdf/1705.08270">pdf</a>, <a href="https://arxiv.org/ps/1705.08270">ps</a>, <a href="https://arxiv.org/format/1705.08270">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.aam.2016.04.006">10.1016/j.aam.2016.04.006 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Generalized Pascal triangle for binomial coefficients of words </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a>, <a href="/search/cs?searchtype=author&query=Stipulanti%2C+M">Manon Stipulanti</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.08270v1-abstract-short" style="display: inline;"> We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi艅ski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo $2$, we des… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08270v1-abstract-full').style.display = 'inline'; document.getElementById('1705.08270v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.08270v1-abstract-full" style="display: none;"> We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi艅ski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo $2$, we describe and study the first properties of the subset of $[0, 1] \times [0, 1]$ associated with this extended Pascal triangle modulo a prime $p$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.08270v1-abstract-full').style.display = 'none'; document.getElementById('1705.08270v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 15 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 28A80 (primary); and 28A78; 11B85; 68R15 (secondary) </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Adv. Appl. Math. 80 (2016) 24-27 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1610.05577">arXiv:1610.05577</a> <span> [<a href="https://arxiv.org/pdf/1610.05577">pdf</a>, <a href="https://arxiv.org/ps/1610.05577">ps</a>, <a href="https://arxiv.org/format/1610.05577">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> The constant of recognizability is computable for primitive morphisms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Durand%2C+F">Fabien Durand</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1610.05577v1-abstract-short" style="display: inline;"> Moss茅 proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be expressed only using the cardinality of the alphabet and the length of the longest image under the morphism of a letter. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1610.05577v1-abstract-full" style="display: none;"> Moss茅 proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be expressed only using the cardinality of the alphabet and the length of the longest image under the morphism of a letter. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.05577v1-abstract-full').style.display = 'none'; document.getElementById('1610.05577v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1507.00206">arXiv:1507.00206</a> <span> [<a href="https://arxiv.org/pdf/1507.00206">pdf</a>, <a href="https://arxiv.org/ps/1507.00206">ps</a>, <a href="https://arxiv.org/format/1507.00206">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Formal Languages and Automata Theory">cs.FL</span> </div> </div> <p class="title is-5 mathjax"> Asymptotic properties of free monoid morphisms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Charlier%2C+E">Emilie Charlier</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1507.00206v2-abstract-short" style="display: inline;"> Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^蠅(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $蟽$ and a coding $蟿$ such that $w =蟿(蟽^蠅(b))$. B… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1507.00206v2-abstract-full').style.display = 'inline'; document.getElementById('1507.00206v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1507.00206v2-abstract-full" style="display: none;"> Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^蠅(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $蟽$ and a coding $蟿$ such that $w =蟿(蟽^蠅(b))$. Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution is an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing $蟽$ and $蟿$ from $f$ and $g$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1507.00206v2-abstract-full').style.display = 'none'; document.getElementById('1507.00206v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 July, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15; 15B36 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.00707">arXiv:1505.00707</a> <span> [<a href="https://arxiv.org/pdf/1505.00707">pdf</a>, <a href="https://arxiv.org/ps/1505.00707">ps</a>, <a href="https://arxiv.org/format/1505.00707">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> </div> </div> <p class="title is-5 mathjax"> Specular sets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Berth%C3%A9%2C+V">Val茅rie Berth茅</a>, <a href="/search/cs?searchtype=author&query=De+Felice%2C+C">Clelia De Felice</a>, <a href="/search/cs?searchtype=author&query=Delecroix%2C+V">Vincent Delecroix</a>, <a href="/search/cs?searchtype=author&query=Dolce%2C+F">Francesco Dolce</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Perrin%2C+D">Dominique Perrin</a>, <a href="/search/cs?searchtype=author&query=reutenauer%2C+C">Christophe reutenauer</a>, <a href="/search/cs?searchtype=author&query=Rindone%2C+G">Giuseppina Rindone</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.00707v2-abstract-short" style="display: inline;"> We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.00707v2-abstract-full" style="display: none;"> We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.00707v2-abstract-full').style.display = 'none'; document.getElementById('1505.00707v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: substantial text overlap with arXiv:1405.3529</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 68R15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1310.0309">arXiv:1310.0309</a> <span> [<a href="https://arxiv.org/pdf/1310.0309">pdf</a>, <a href="https://arxiv.org/ps/1310.0309">ps</a>, <a href="https://arxiv.org/format/1310.0309">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Formal Languages and Automata Theory">cs.FL</span> </div> </div> <p class="title is-5 mathjax"> An analogue of Cobham's theorem for graph directed iterated function systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Charlier%2C+E">Emilie Charlier</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Rigo%2C+M">Michel Rigo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1310.0309v3-abstract-short" style="display: inline;"> Feng and Wang showed that two homogeneous iterated function systems in $\mathbb{R}$ with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated function systems in $\mathbb{R}^n$ with contraction ratios that are of the form $\frac{1}尾$, for integers $尾$. By using a result of Boigelot et al., this allows… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.0309v3-abstract-full').style.display = 'inline'; document.getElementById('1310.0309v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1310.0309v3-abstract-full" style="display: none;"> Feng and Wang showed that two homogeneous iterated function systems in $\mathbb{R}$ with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated function systems in $\mathbb{R}^n$ with contraction ratios that are of the form $\frac{1}尾$, for integers $尾$. By using a result of Boigelot et al., this allows us to give a proof of a conjecture of Adamczewski and Bell. In doing so, we link the graph directed iterated function systems to B眉chi automata. In particular, this link extends to real numbers $尾$. We introduce a logical formalism that permits to characterize sets of $\mathbb{R}^n$ whose representations in base $尾$ are recognized by some B眉chi automata. This result depends on the algebraic properties of the base: $尾$ being a Pisot or a Parry number. The main motivation of this work is to draw a general picture representing the different frameworks where an analogue of Cobham's theorem is known. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.0309v3-abstract-full').style.display = 'none'; document.getElementById('1310.0309v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages; updated version, including a new introduction and some new references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 28A80 (primary); and 28A78; 11B85; 68Q70; 11K16 (secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1308.4260">arXiv:1308.4260</a> <span> [<a href="https://arxiv.org/pdf/1308.4260">pdf</a>, <a href="https://arxiv.org/ps/1308.4260">ps</a>, <a href="https://arxiv.org/format/1308.4260">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Formal Languages and Automata Theory">cs.FL</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00605-014-0721-4">10.1007/s00605-014-0721-4 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Acyclic, connected and tree sets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Berth%C3%A9%2C+V">Valerie Berth茅</a>, <a href="/search/cs?searchtype=author&query=De+Felice%2C+C">Clelia De Felice</a>, <a href="/search/cs?searchtype=author&query=Dolce%2C+F">Francesco Dolce</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Perrin%2C+D">Dominique Perrin</a>, <a href="/search/cs?searchtype=author&query=Reutenauer%2C+C">Christophe Reutenauer</a>, <a href="/search/cs?searchtype=author&query=Rindone%2C+G">Giuseppina Rindone</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1308.4260v6-abstract-short" style="display: inline;"> Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected or a tree. We prove that in a uniformly recurrent tree set, the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.4260v6-abstract-full').style.display = 'inline'; document.getElementById('1308.4260v6-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1308.4260v6-abstract-full" style="display: none;"> Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected or a tree. We prove that in a uniformly recurrent tree set, the sets of first return words are bases of the free group on the alphabet. Concerning acyclic sets, we prove as a main result that a set $F$ is acyclic if and only if any bifix code included in $F$ is a basis of the subgroup that it generates. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1308.4260v6-abstract-full').style.display = 'none'; document.getElementById('1308.4260v6-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 August, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: substantial text overlap with arXiv:1305.0127, arXiv:1011.5369, Monatsh. Math. (2015)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1305.0434">arXiv:1305.0434</a> <span> [<a href="https://arxiv.org/pdf/1305.0434">pdf</a>, <a href="https://arxiv.org/ps/1305.0434">ps</a>, <a href="https://arxiv.org/format/1305.0434">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> An $S$-adic characterization of minimal subshifts with first difference of complexity $1 \leq p(n+1) - p(n) \leq 2$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1305.0434v1-abstract-short" style="display: inline;"> In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is $S$-adic with $\card S \leq 3^{27}$. In this paper, we improve this result by giving an $S$-adic charaterization of these subshifts with a set $S$ of 5 morphisms, solving by this way the $S$-adic conjecture for this particular case. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1305.0434v1-abstract-full" style="display: none;"> In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is $S$-adic with $\card S \leq 3^{27}$. In this paper, we improve this result by giving an $S$-adic charaterization of these subshifts with a set $S$ of 5 morphisms, solving by this way the $S$-adic conjecture for this particular case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.0434v1-abstract-full').style.display = 'none'; document.getElementById('1305.0434v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2013. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1305.0127">arXiv:1305.0127</a> <span> [<a href="https://arxiv.org/pdf/1305.0127">pdf</a>, <a href="https://arxiv.org/ps/1305.0127">ps</a>, <a href="https://arxiv.org/format/1305.0127">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> The finite index basis property </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Berth%C3%A9%2C+V">Val茅rie Berth茅</a>, <a href="/search/cs?searchtype=author&query=De+Felice%2C+C">Clelia De Felice</a>, <a href="/search/cs?searchtype=author&query=Dolce%2C+F">Francesco Dolce</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Perrin%2C+D">Dominique Perrin</a>, <a href="/search/cs?searchtype=author&query=Reutenauer%2C+C">Christophe Reutenauer</a>, <a href="/search/cs?searchtype=author&query=Rindone%2C+G">Giuseppina Rindone</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1305.0127v7-abstract-short" style="display: inline;"> We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namemly the class of tre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.0127v7-abstract-full').style.display = 'inline'; document.getElementById('1305.0127v7-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1305.0127v7-abstract-full" style="display: none;"> We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namemly the class of tree sets. We prove as a main result that for a uniformly recurrent tree set $F$, a finite bifix code $X$ on the alphabet $A$ is $F$-maximal of $F$-degree $d$ if and only if it is the basis of a subgroup of index $d$ of the free group on $A$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.0127v7-abstract-full').style.display = 'none'; document.getElementById('1305.0127v7-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:1011.5369, arXiv:1305.0120</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Pure Appl. Algebra, 219 (2015) 2521-2537 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1208.6376">arXiv:1208.6376</a> <span> [<a href="https://arxiv.org/pdf/1208.6376">pdf</a>, <a href="https://arxiv.org/ps/1208.6376">ps</a>, <a href="https://arxiv.org/format/1208.6376">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Discrete Mathematics">cs.DM</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> Towards a statement of the S-adic conjecture through examples </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Durand%2C+F">Fabien Durand</a>, <a href="/search/cs?searchtype=author&query=Leroy%2C+J">Julien Leroy</a>, <a href="/search/cs?searchtype=author&query=Richomme%2C+G">Gw茅na毛l Richomme</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1208.6376v1-abstract-short" style="display: inline;"> The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to wh… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.6376v1-abstract-full').style.display = 'inline'; document.getElementById('1208.6376v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1208.6376v1-abstract-full" style="display: none;"> The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be "a good Condition $C$". <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.6376v1-abstract-full').style.display = 'none'; document.getElementById('1208.6376v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25</span> </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a 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