Complementary symmetric Rote sequences: the critical exponent and the recurrence function

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00341424" target="_blank" >RIV/68407700:21340/20:00341424 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.23638/DMTCS-22-1-20" target="_blank" >https://doi.org/10.23638/DMTCS-22-1-20</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23638/DMTCS-22-1-20" target="_blank" >10.23638/DMTCS-22-1-20</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Complementary symmetric Rote sequences: the critical exponent and the recurrence function

Popis výsledku v původním jazyce

We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the corresponding standard Sturmian sequences. The results are based on a thorough study of return words to bispecial factors of Sturmian sequences. Using the formula for the critical exponent, we describe all complementary symmetric Rote sequences with the critical exponent less than or equal to 3, and we show that there are uncountably many complementary symmetric Rote sequences with the critical exponent less than the critical exponent of the Fibonacci sequence. Our study is motivated by a conjecture on sequences rich in palindromes formulated by Baranwal and Shallit. Its recent solution by Curie, Mol, and Rampersad uses two particular complementary symmetric Rote sequences.

Název v anglickém jazyce

Complementary symmetric Rote sequences: the critical exponent and the recurrence function

Popis výsledku anglicky

We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the corresponding standard Sturmian sequences. The results are based on a thorough study of return words to bispecial factors of Sturmian sequences. Using the formula for the critical exponent, we describe all complementary symmetric Rote sequences with the critical exponent less than or equal to 3, and we show that there are uncountably many complementary symmetric Rote sequences with the critical exponent less than the critical exponent of the Fibonacci sequence. Our study is motivated by a conjecture on sequences rich in palindromes formulated by Baranwal and Shallit. Its recent solution by Curie, Mol, and Rampersad uses two particular complementary symmetric Rote sequences.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Discrete Mathematics and Theoretical Computer Science

ISSN

1462-7264

e-ISSN

1365-8050

Svazek periodika

22

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

33

Strana od-do

—

Kód UT WoS článku

000561191500019

EID výsledku v databázi Scopus

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