A unique extension of rich words

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00354375" target="_blank" >RIV/68407700:21340/21:00354375 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.tcs.2021.10.004" target="_blank" >https://doi.org/10.1016/j.tcs.2021.10.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2021.10.004" target="_blank" >10.1016/j.tcs.2021.10.004</a>

Result language
angličtina
Original language name
A unique extension of rich words
Original language description
A word w is called rich if it contains |w|+1 palindromic factors, including the empty word. We say that a rich word w can be extended in at least two ways if there are two distinct letters x, y such that wx, wy are rich. Let R denote the set of all rich words. Given w in R let K(w) denote the set of all words u such that wu is in R and wu can be extended in at least two ways. Let o(w) = min{|u| : u in K(w)} and let phi(n) = max {o(w) : w in R and |w|=n}, where n>0. Vesti (2014) showed that phi(n) < 2n+1. In other words, it says that for each w in R there is a word u with |u|<2|w| such that wu is in R and wu can be extended in at least two ways. We prove that phi(n)<n+1 and that lim sup phi(n)/n is greater than or equal to 2/9 as n tends to infinity. The results hold for each finite alphabet having at least two letters.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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