About: Numbers with integer expansion in the system with negative base

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set $\Z_{-\beta}$ of numbers whose representation uses only non-negative powers of $-\beta$, the so-called $(-\beta)$-integers. We describe the distances between consecutive elements of $\Z_{-\beta}$. In case that this set is non-trivial we associate to $\beta$ an infinite word $\boldsymbol{v}_{-\beta}$ over an (in general infinite) alphabet. The self-similarity of $\Z_{-\beta}$, i.e., the property $-\beta\Z_{-\beta}\subset \Z_{-\beta}$, allows us to find a morphism under which $\boldsymbol{v}_{-\beta}$ is invariant. On the example of two cubic irrational bases $\beta$ we demonstrate the difference between Rauzy fractals generated by $(-\beta)$-integers and by $\beta$-integers. In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set $\Z_{-\beta}$ of numbers whose representation uses only non-negative powers of $-\beta$, the so-called $(-\beta)$-integers. We describe the distances between consecutive elements of $\Z_{-\beta}$. In case that this set is non-trivial we associate to $\beta$ an infinite word $\boldsymbol{v}_{-\beta}$ over an (in general infinite) alphabet. The self-similarity of $\Z_{-\beta}$, i.e., the property $-\beta\Z_{-\beta}\subset \Z_{-\beta}$, allows us to find a morphism under which $\boldsymbol{v}_{-\beta}$ is invariant. On the example of two cubic irrational bases $\beta$ we demonstrate the difference between Rauzy fractals generated by $(-\beta)$-integers and by $\beta$-integers. (en)
Title	Numbers with integer expansion in the system with negative base Numbers with integer expansion in the system with negative base (en)
skos:prefLabel	Numbers with integer expansion in the system with negative base Numbers with integer expansion in the system with negative base (en)
skos:notation	RIV/68407700:21340/12:00186826!RIV13-GA0-21340___
http://linked.open...avai/predkladatel	Fakulta jaderná a fyzikálně inženýrská
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(GA201/09/0584), P(LC06002), S, Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Masáková, Zuzana Dombek, Daniel Pelantová, Edita Ambrož, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	154963
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/12:00186826
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	numeration system; negative base; Pisot numbers; morphism (en)
http://linked.open.../riv/klicoveSlovo	Pisot numbers negative base numeration system morphism
http://linked.open...odStatuVydavatele	PL - Polská republika
http://linked.open...ontrolniKodProRIV	[EF5B755A6AE7]
http://linked.open...i/riv/nazevZdroje	Functiones et Approximatio, Commentarii Mathematici
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	4 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraic and combinatorial aspects of aperiodic structures Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Ambrož, Petr Dombek, Daniel Masáková, Zuzana Pelantová, Edita
http://linked.open...n/vavai/riv/zamer	Matematické, počítačové a experimentální metody ve fyzice
issn	0208-6573
number of pages	26 (xsd:int)
http://bibframe.org/vocab/doi	10.7169/facm/2012.47.2.8
http://localhost/t...ganizacniJednotka	21340
is http://linked.open...avai/riv/vysledek of	Numbers with integer expansion in the system with negative base

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