Binary patterns in the Prouhet-Thue-Morse sequence

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00119378" target="_blank" >RIV/00216224:14310/21:00119378 - isvavai.cz</a>
Result on the web
<a href="https://dmtcs.episciences.org/8398" target="_blank" >https://dmtcs.episciences.org/8398</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/dmtcs.5460" target="_blank" >10.46298/dmtcs.5460</a>

Result language
angličtina
Original language name
Binary patterns in the Prouhet-Thue-Morse sequence
Original language description
We show that, with the exception of the words a(2)ba(2) and b(2)ab(2), all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself.
Czech name
—
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
—
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/GA19-12790S" target="_blank" >GA19-12790S: Effective characterizations of classes of finite semigroups and formal languages</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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