On minimal critical exponent of balanced sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00362043" target="_blank" >RIV/68407700:21340/22:00362043 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.tcs.2022.04.021" target="_blank" >https://doi.org/10.1016/j.tcs.2022.04.021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2022.04.021" target="_blank" >10.1016/j.tcs.2022.04.021</a>

Result language
angličtina
Original language name
On minimal critical exponent of balanced sequences
Original language description
We study the threshold between avoidable and unavoidable repetitions in infinite balanced sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and Vandomme says that the minimal critical exponent of balanced sequences over the alphabet of size d>4 equals (d-2)/(d-3). This conjecture is known to hold for d in {5, 6, 7,8,9,10}. We refute this conjecture by showing that the picture is different for bigger alphabets. We prove that critical exponents of balanced sequences over an alphabet of size d>10 are lower bounded by (d-1)/(d-2) and this bound is attained for all even numbers d>11. According to this result, we conjecture that the least critical exponent of a balanced sequence over d letters is (d-1)/(d-2) for all d>10.
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
10101 - Pure mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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