Description of spectra of quadratic Pisot units

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00219584" target="_blank" >RIV/68407700:21340/15:00219584 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jnt.2014.11.011" target="_blank" >http://dx.doi.org/10.1016/j.jnt.2014.11.011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2014.11.011" target="_blank" >10.1016/j.jnt.2014.11.011</a>

Result language
angličtina
Original language name
Description of spectra of quadratic Pisot units
Original language description
The spectrum of a real number $beta>1$ is the set $X^{m}(beta)$ of $p(beta)$ where $p$ ranges over all polynomials with coefficients restricted to $A={0,1,dots,m}$. For a quadratic Pisot unit $beta$, we determine the values of all distances between consecutive points and their corresponding frequencies, by recasting the spectra in the frame of the cut-and-project scheme. We also show that shifting the set $A$ of digits so that it contains at least one negative element, or considering negative base $-beta$ instead of $beta$, the gap sequence of the generalized spectrum is a coding of an exchange of three intervals.
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
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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