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- W3205034402 abstract "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 $win R$, let $K(w)$ denote the set of all words such that if $uin K(w)$ then $wuin R$ and $wu$ can be extended in at least two ways. Let $omega(w)=min{| u| mid uin K(w)}$ and let $phi(n)=max{omega(w)mid win Rmbox{ and }| w|=n}$, where $n>0$. Vesti (2014) showed that $phi(n)leq 2n$. In other words, it says that for each $win R$ there is a word $u$ with $| u|leq 2| w|$ such that $wuin R$ and $wu$ can be extended in at least two ways. We prove that $phi(n)leq n$. In addition we prove that for each real constant $c>0$ and each integer $m>0$ there is $n>m$ such that $phi(n)geq (frac{2}{9}-c)n$. The results hold for each finite alphabet having at least two letters." @default.
- W3205034402 created "2021-10-25" @default.
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- W3205034402 date "2021-12-01" @default.
- W3205034402 modified "2023-09-24" @default.
- W3205034402 title "A unique extension of rich words" @default.
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- W3205034402 doi "https://doi.org/10.1016/j.tcs.2021.10.004" @default.
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