Generalized Thue-Morse words and palindromic richness

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F12%3A00184068" target="_blank" >RIV/68407700:21240/12:00184068 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Generalized Thue-Morse words and palindromic richness
Original language description
We prove that the generalized Thue-Morse word $mathbf{t}_{b,m}$ defined for $b geq 2$ and $m geq 1$ as $mathbf{t}_{b,m} = left ( s_b(n) mod m right )_{n=0}^{+infty}$, where $s_b(n)$ denotes the sum of digits in the base-$b$ representation of theinteger $n$, has its language closed under all elements of a group $D_m$ isomorphic to the dihedral group of order $2m$ consisting of morphisms and antimorphisms. Considering simultaneously antimorphisms $Theta in D_m$, we show that $mathbf{t}_{b,m}$is saturated by $Theta$-palindromes up to the highest possible level. Using the terminology generalizing the notion of palindromic richness for more antimorphisms recently introduced by the author and E. Pelantov'a, we show that $mathbf{t}_{b,m}$ is $D_m$-rich. We also calculate the factor complexity of $mathbf{t}_{b,m}$.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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