The asymptotic repetition threshold of sequences rich in palindromes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F25%3A00385808" target="_blank" >RIV/68407700:21240/25:00385808 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/25:00385808
Result on the web
<a href="https://doi.org/10.1016/j.ejc.2025.104124" target="_blank" >https://doi.org/10.1016/j.ejc.2025.104124</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2025.104124" target="_blank" >10.1016/j.ejc.2025.104124</a>

Result language
angličtina
Original language name
The asymptotic repetition threshold of sequences rich in palindromes
Original language description
he asymptotic critical exponent measures for a sequence the maximum repetition rate of factors of growing length. The infimum of asymptotic critical exponents of sequences of a certain class is called the asymptotic repetition threshold of that class. On the one hand, if we consider the class of all d-ary sequences with d>1, then the asymptotic repetition threshold is equal to one, independently of the alphabet size. On the other hand, for the class of episturmian sequences, the repetition threshold depends on the alphabet size. We focus on rich sequences, i.e., sequences whose factors contain the maximum possible number of distinct palindromes. The class of episturmian sequences forms a subclass of rich sequences. We prove that the asymptotic repetition threshold for the class of rich recurrent d-ary sequences, with d>1, is equal to two, independently of the alphabet size.
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

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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