On balanced sequences and their critical exponent

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00362049" target="_blank" >RIV/68407700:21240/23:00362049 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/23:00362049
Result on the web
<a href="https://doi.org/10.1016/j.tcs.2022.10.014" target="_blank" >https://doi.org/10.1016/j.tcs.2022.10.014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2022.10.014" target="_blank" >10.1016/j.tcs.2022.10.014</a>

Result language
angličtina
Original language name
On balanced sequences and their critical exponent
Original language description
We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we focus on return words to its factors. We deduce a method computing critical exponent and asymptotic critical exponent of balanced sequences provided the associated Sturmian sequence u has a quadratic slope. The method is based on looking for the shortest return words to bispecial factors in v. We illustrate our method on several examples, in particular we confirm a conjecture of Rampersad, Shallit and Vandomme that two specific sequences have the least critical exponent among all balanced sequences over 9- resp. 10-letter alphabets.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)