On Sturmian substitutions closed under derivation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00353259" target="_blank" >RIV/68407700:21240/21:00353259 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/21:00353259
Result on the web
<a href="https://doi.org/10.1016/J.TCS.2021.03.033" target="_blank" >https://doi.org/10.1016/J.TCS.2021.03.033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/J.TCS.2021.03.033" target="_blank" >10.1016/J.TCS.2021.03.033</a>

Result language
angličtina
Original language name
On Sturmian substitutions closed under derivation
Original language description
Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${bf u}$ can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${bf d_{bf u}}(w)$ and called the derived sequence to $w$ in ${bf u}$. If $w$ is a prefix of a fixed point ${bf u}$ of a primitive substitution $varphi$, then by Durand's result from 1998, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a primitive substitution $psi$ as well. For a non-prefix factor $w$, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a substitution only exceptionally. To study this phenomenon we introduce a new notion: A finite set $M $ of substitutions is said to be closed under derivation if the derived sequence ${bf d_{bf u}}(w)$ to any factor $w$ of any fixed point ${bf u}$ of $varphi in M$ is fixed by a morphism $psi in M$. In our article we characterize the Sturmian substitutions which belong to a set $M$ closed under derivation. The characterization uses either the slope and the intercept of its fixed point or its S-adic representation.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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