Combinatorial properties of infinite words associated with cut and project sequences

Result code in 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>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Combinatorial properties of infinite words associated with cut and project sequences

Original language description

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 $2n+1$.

Czech name

Combinatorial properties of infinite words associated with cut and project sequences

Czech description

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 $2n+1$.

Type

J_x - 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/GA201%2F01%2F0130" target="_blank" >GA201/01/0130: Some aspects of quantum group and self-similar aperiodic structures</a><br>

Continuities

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

Publication year

2003

Confidentiality

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

Name of the periodical

J. Theor. Nombres Bordeaux

ISSN

1246-7405

e-ISSN

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Volume of the periodical

15

Issue of the periodical within the volume

6

Country of publishing house

FR - FRANCE

Number of pages

29

Pages from-to

697-725

UT code for WoS article

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EID of the result in the Scopus database

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