Proof of the Brlek-Reutenauer conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00201614" target="_blank" >RIV/68407700:21340/13:00201614 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/13:00201614
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2012.12.024" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2012.12.024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2012.12.024" target="_blank" >10.1016/j.tcs.2012.12.024</a>

Result language
angličtina
Original language name
Proof of the 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)= sum_{n=0}^{+infty}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)-P_u(n+1), where C_u(n) and P_u(n) are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.
Czech name
—
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
<a href="/en/project/GA201%2F09%2F0584" target="_blank" >GA201/09/0584: Algebraic and combinatorial aspects of aperiodic structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)<br>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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