The repetition threshold of episturmian sequences

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The repetition threshold of episturmian sequences

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The repetition threshold of episturmian sequences

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

1095-9971

Svazek periodika

120

Číslo periodika v rámci svazku

104001

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

—

Kód UT WoS článku

001254812300001

EID výsledku v databázi Scopus

2-s2.0-85194957435