On Brlek-Reutenauer conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00183922" target="_blank" >RIV/68407700:21340/11:00183922 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/11:00183922
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2011.06.031" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2011.06.031</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2011.06.031" target="_blank" >10.1016/j.tcs.2011.06.031</a>

Result language
angličtina
Original language name
On Brlek-Reutenauer conjecture
Original language description
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = Sigma(+infinity)(n=0) T(u)(n) in which D(u) denotes the defect of u and T(u)(n) denotes C(u)(n + 1) - C(u)(n) + 2 - P(u)(n + 1) -P(u)(n), where C(u) and P(u) are the factor and palindromic complexity of u, respectively. BrIek and Reutenauer verified their conjecture for periodic infinite words. Using their result, we prove the conjecture for uniformly recurrent words. Moreover, we summarize results and some open problems related to defects, which may be useful for the proof of the Brlek-Reutenauer conjecture in full generality.
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
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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