The repetition threshold of episturmian sequences

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00382219" target="_blank" >RIV/68407700:21340/24:00382219 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.ejc.2024.104001" target="_blank" >https://doi.org/10.1016/j.ejc.2024.104001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ejc.2024.104001" target="_blank" >10.1016/j.ejc.2024.104001</a>

Result language

angličtina

Original language name

The repetition threshold of episturmian sequences

Original language description

The repetition threshold of a class C of infinite d-ary sequences is the smallest real number r such that in the class C there exists a sequence that avoids e-powers for all e > r. This notion was introduced by Dejean in 1972 for the class of all sequences over a d-letter alphabet. Thanks to the effort of many authors over more than 30 years, the precise value of the repetition threshold in this class is known for every d is an element of N. The repetition threshold for the class of Sturmian sequences was determined by Carpi and de Luca in 2000. Sturmian sequences may be equivalently defined in various ways, therefore there exist many generalizations to larger alphabets. Rampersad, Shallit and Vandome in 2020 initiated a study of the repetition threshold for the class of balanced sequences - one of the possible generalizations of Sturmian sequences. Here, we focus on the class of d-ary episturmian sequences - another generalization of Sturmian sequences introduced by Droubay, Justin and Pirillo in 2001. We show that the repetition threshold of this class is reached by the d-bonacci sequence and its value equals 2+ 1/t-1 positive root of the polynomial x(d) - x(d-1) - <middle dot> <middle dot> <middle dot> - x - 1. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

1095-9971

Volume of the periodical

120

Issue of the periodical within the volume

104001

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

15

Pages from-to

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UT code for WoS article

001254812300001

EID of the result in the Scopus database

2-s2.0-85194957435