About: Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study some arithmetical and combinatorial properties of $\beta$-integers for $\beta$ being the larger root of the equation $x^2=mx-n, m,n \in \mathbb N, m \geq n+2\geq 3$. We determine with the accuracy of $\pm 1$ the maximal number of $\beta$-fractional positions, which may arise as a~result of addition of two $\beta$-integers. For the infinite word $u_\beta$ coding distances between the consecutive $\beta$-integers, we determine precisely also the balance. The word $u_\beta$ is the only fixed point of the morphism $A \to A^{m-1}B$ and $B\to A^{m-n-1}B$. In the case $n=1$, the corresponding infinite word $u_\beta$ is sturmian, and, therefore, $1$-balanced. On the simplest non-sturmian example with $n\geq 2$, we illustrate how closely the balance and the arithmetical properties of $\beta$-integers are related. We study some arithmetical and combinatorial properties of $\beta$-integers for $\beta$ being the larger root of the equation $x^2=mx-n, m,n \in \mathbb N, m \geq n+2\geq 3$. We determine with the accuracy of $\pm 1$ the maximal number of $\beta$-fractional positions, which may arise as a~result of addition of two $\beta$-integers. For the infinite word $u_\beta$ coding distances between the consecutive $\beta$-integers, we determine precisely also the balance. The word $u_\beta$ is the only fixed point of the morphism $A \to A^{m-1}B$ and $B\to A^{m-n-1}B$. In the case $n=1$, the corresponding infinite word $u_\beta$ is sturmian, and, therefore, $1$-balanced. On the simplest non-sturmian example with $n\geq 2$, we illustrate how closely the balance and the arithmetical properties of $\beta$-integers are related. (en) Studujeme některé aritmetické a kombinatorické vlastnosti beta celých čísel v případech, kdy beta je větší z kořenů kvadratické rovnice $x^2=mx-n, m,n \in \mathbb N, m \geq n+2\geq 3$. Určujeme s přesností na $\pm 1$ maximální délku zlomkové části, která může vzniknout součtem dvou beta celých čísel. Pro nekonečné slovo $u_\beta$, které kóduje mezery mezi beta celými čísly, určujeme přesně hodnotu balance. Slovo $u_\beta$ je jediným pevným slovem morfizmu $A \to A^{m-1}B$ and $B\to A^{m-n-1}B$. (cs)
Title	Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers Kombinatorické a aritmetické vlastnosti nekonečných slov spojených s nejednoduchými kvadratickými Parryho čísly. (cs) Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers (en)
skos:prefLabel	Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers Kombinatorické a aritmetické vlastnosti nekonečných slov spojených s nejednoduchými kvadratickými Parryho čísly. (cs) Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers (en)
skos:notation	RIV/68407700:21340/07:04137464!RIV08-GA0-21340___
http://linked.open.../vavai/riv/strany	307;328
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/05/0169), Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika	41
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Pelantová, Edita Turek, Ondřej Balková, Lubomíra
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	414138
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/07:04137464
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Parry number, beta-integers, balance property, fractional part (en)
http://linked.open.../riv/klicoveSlovo	balance property Parry number beta-integers fractional part
http://linked.open...odStatuVydavatele	FR - Francouzská republika
http://linked.open...ontrolniKodProRIV	[23FC6A819168]
http://linked.open...i/riv/nazevZdroje	RAIRO - Theoretical Informatics and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraic and combinatorial aspects of aperiodic structures
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	2007
http://linked.open...iv/tvurceVysledku	Balková, Lubomíra Pelantová, Edita Turek, Ondřej
http://linked.open...n/vavai/riv/zamer	Matematické, počítačové a experimentální metody ve fyzice
issn	0988-3754
number of pages	22 (xsd:int)
http://localhost/t...ganizacniJednotka	21340
is http://linked.open...avai/riv/vysledek of	Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers

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