Combinatorial properties of infinite words associated with cut and project sequences

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F03%3A04105350" target="_blank" >RIV/68407700:21340/03:04105350 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Combinatorial properties of infinite words associated with cut and project sequences

Popis výsledku v původním jazyce

The aim of this article is to study certain combinatorial properties of infinite binary and ternary words associated to cut-and-project sequences. We consider here the cut-and-project scheme in two dimensions with general orientation of the projecting subspaces. We prove that a cut-and-project sequence arising in such a setting has always either two or three types of distances between adjacent points. A cut-and-project sequence thus determines in a natural way a symbolic sequence (infinite word) in twoor three letters. In fact, these letter can be constructed also by a coding of a 2- or 3-interval exchange transformation. According to the complexity the cut-and-project construction includes words with complexity $n+1$, $n+const.$ and $2n+1$. The wordson two letter alphabet have complexity $n+1$ and thus are Sturmian. The ternary words associated to the cut-and-project sequences have complexity $n+const.$ or $2n+1$.

Název v anglickém jazyce

Combinatorial properties of infinite words associated with cut and project sequences

Popis výsledku anglicky

The aim of this article is to study certain combinatorial properties of infinite binary and ternary words associated to cut-and-project sequences. We consider here the cut-and-project scheme in two dimensions with general orientation of the projecting subspaces. We prove that a cut-and-project sequence arising in such a setting has always either two or three types of distances between adjacent points. A cut-and-project sequence thus determines in a natural way a symbolic sequence (infinite word) in twoor three letters. In fact, these letter can be constructed also by a coding of a 2- or 3-interval exchange transformation. According to the complexity the cut-and-project construction includes words with complexity $n+1$, $n+const.$ and $2n+1$. The wordson two letter alphabet have complexity $n+1$ and thus are Sturmian. The ternary words associated to the cut-and-project sequences have complexity $n+const.$ or $2n+1$.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F01%2F0130" target="_blank" >GA201/01/0130: Některé aspekty kvantových grup a selfsimilaritních aperiodických struktur</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2003

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

J. Theor. Nombres Bordeaux

ISSN

1246-7405

e-ISSN

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Svazek periodika

15

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

29

Strana od-do

697-725

Kód UT WoS článku

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EID výsledku v databázi Scopus

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