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- W3100415903 abstract "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 $Factor(w)$ 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 common 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 ${u,v}subseteq Factor(w)$. 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 ${w_1,w_2}subseteq Factor(w)$ then there exists also a rich word $bar w$ such that ${w_1,w_2}subseteq Factor(bar w)$ 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 $w_1,w_2$." @default.
- W3100415903 created "2020-11-23" @default.
- W3100415903 creator A5030995240 @default.
- W3100415903 date "2019-01-01" @default.
- W3100415903 modified "2023-09-23" @default.
- W3100415903 title "Rich Words Containing Two Given Factors" @default.
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- W3100415903 doi "https://doi.org/10.1007/978-3-030-28796-2_23" @default.
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