Asymptotic repetitive threshold of balanced sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00362047" target="_blank" >RIV/68407700:21340/23:00362047 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/mcom/3816" target="_blank" >https://doi.org/10.1090/mcom/3816</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/mcom/3816" target="_blank" >10.1090/mcom/3816</a>

Result language
angličtina
Original language name
Asymptotic repetitive threshold of balanced sequences
Original language description
The critical exponent E(u) of an infinite sequence u over a finite alphabet expresses the maximal repetition of a factor in u. By the famous Dejean's theorem, E(u) is less or equal to 1+1/(d-1) for every d-ary sequence u. We define the asymptotic critical exponent E*(u) as the upper limit of the maximal repetition of factors of length n. We show that for any d>1 there exists a d-ary sequence u having E*(u) arbitrarily close to 1. Then we focus on the class of d-ary balanced sequences. In this class, the values E*(u)$ are bounded from below by a threshold strictly bigger than 1. We provide a method which enables us to find a d-ary balanced sequence with the least asymptotic critical exponent for 1<d<11.
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
<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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)