Palindromic length and reduction of powers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00361402" target="_blank" >RIV/68407700:21340/22:00361402 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.tcs.2022.07.015" target="_blank" >https://doi.org/10.1016/j.tcs.2022.07.015</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2022.07.015" target="_blank" >10.1016/j.tcs.2022.07.015</a>

Result language
angličtina
Original language name
Palindromic length and reduction of powers
Original language description
The palindromic length of a finite word v is the minimum number of palindromes whose concatenation is equal to v. It was conjectured in 2013 that for every aperiodic infinite word x, the palindromic length of its factors is not bounded. Let x be an infinite aperiodic word with a bounded palindromic length and containing infinitely many occurrences of the fifth power u5 of some word u. In this paper, we prove that we can erase from x extra powers of u and of its reversal uR to get another infinite aperiodic word of bounded palindromic length which does not contain u5 nor (uR)5. This result is not sufficient to prove that x does not exist but may give a hint for this proof.(c) 2022 Elsevier B.V. All rights reserved.
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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