Palindromic factorization of rich words

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00361403" target="_blank" >RIV/68407700:21340/22:00361403 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2022.03.030" target="_blank" >https://doi.org/10.1016/j.dam.2022.03.030</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2022.03.030" target="_blank" >10.1016/j.dam.2022.03.030</a>

Result language
angličtina
Original language name
Palindromic factorization of rich words
Original language description
A finite word w is called rich if it contains |w|+1 distinct palindromic factors including the empty word. For every finite rich word w there are distinct nonempty palindromes w(1), w(2), ..., w(p) such that w = w(p)w(p-1) ... w(1) and w(i) is the longest palindromic suffix of w(p)w(p-1) ... w(i), where 1 <= i <= p. This palindromic factorization is called UPS-factorization. Let luf(w) = p be the length of UPS-factorization of w. In 2017, it was proved that there is a constant c such that if w is a finite rich word and n=|w| then luf(w) <= cn/(ln n). We improve this result as follows: There are positive constants m, k such that if w is a finite rich word and n=|w| then luf(w) <= m*n/exp(k*root(ln n)). The constants c, m, k depend on the size of the alphabet.
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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