Languages invariant under more symmetries: overlapping factors versus palindromic richness

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00186784" target="_blank" >RIV/68407700:21340/13:00186784 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/13:00186784
Result on the web
<a href="http://dx.doi.org/10.1016/j.disc.2013.07.002" target="_blank" >http://dx.doi.org/10.1016/j.disc.2013.07.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2013.07.002" target="_blank" >10.1016/j.disc.2013.07.002</a>

Result language
angličtina
Original language name
Languages invariant under more symmetries: overlapping factors versus palindromic richness
Original language description
Factor complexity $mathcal{C}$ and palindromic complexity $mathcal{P}$ of infinite words with language closed under reversal are known to be related by the inequality $mathcal{P}(n) + mathcal{P}(n+1) leq 2 + mathcal{C}(n+1)-mathcal{C}(n)$ for any $nin mathbb{N}$,. Words for which the equality is attained for any $n$ are usually called rich in palindromes. We show that rich words contain infinitely many overlapping factors. We study words whose languages are invariant under a finite group $G$ of symmetries. For such words we prove a stronger version of the above inequality. We introduce the notion of $G$-palindromic richness and give several examples of $G$-rich words, including the Thue-Morse sequence as well.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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