Rich Words Containing Two Given Factors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00335008" target="_blank" >RIV/68407700:21340/19:00335008 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-030-28796-2_23" target="_blank" >http://dx.doi.org/10.1007/978-3-030-28796-2_23</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-28796-2_23" target="_blank" >10.1007/978-3-030-28796-2_23</a>

Result language
angličtina
Original language name
Rich Words Containing Two Given Factors
Original language description
A finite word $w$ with $vert wvert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called emph{rich}. Let $F(w)$ be the set of factors of the word $w$. It is known that there are pairs of rich words that cannot be factors of a same rich word. However it is an open question how to decide for a given pair of rich words $u,v$ if there is a rich word $w$ such that ${u,v}subseteq F(w)$. We present a response to this open question: If $w_1, w_2,w$ are rich words, $m=max{{vert w_1vert,vert w_2vert}}$, and ${w_1,w_2}subseteq F(w)$ then there exists also a rich word $bar w$ such that ${w_1,w_2}subseteq F(bar w)$ and $vert bar wvertleq m2^{k(m)+2}$, where $k(m)=(q+1)m^2(4q^{10}m)^{log_2{m}}$ and $q$ is the size of the alphabet. Hence it is enough to check all rich words of length equal or lower to $m2^{k(m)+2}$ in order to decide if there is a rich word containing factors $w_1,w_2$.
Czech name
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Czech description
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Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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