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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)
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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)
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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)
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skos:notation
| - RIV/68407700:21340/07:04137464!RIV08-GA0-21340___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/05/0169), Z(MSM6840770039)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21340/07:04137464
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Parry number, beta-integers, balance property, fractional part (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - FR - Francouzská republika
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - RAIRO - Theoretical Informatics and Applications
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Balková, Lubomíra
- Pelantová, Edita
- Turek, Ondřej
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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