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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

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

<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>

Continuities

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

Publication year

2020

Confidentiality

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

Name of the periodical

Discrete Mathematics and Theoretical Computer Science

ISSN

1462-7264

e-ISSN

1365-8050

Volume of the periodical

22

Issue of the periodical within the volume

1

Country of publishing house

FR - FRANCE

Number of pages

33

Pages from-to

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UT code for WoS article

000561191500019

EID of the result in the Scopus database

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