Geodesic
The lexicographically least binary rich word achieving the repetition threshold
James D. Currie ; Narad Rampersad1
1Department of Mathematics and Statistics, University of Winnipeg
The electronic journal of combinatorics, Tome 31 (2024) no. 4
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

A word is rich if each of its length $n$ factors contains $n$ distinct non-empty palindromes. For a language ${\mathcal L}$, the repetition threshold of ${\mathcal L}$ is defined by$$\text{RT}({\mathcal L})=\sup\{k: \text{ every infinite word of ${\mathcal L}$ contains a $k$-power}\}.$$Currie et al. (2020) proved that the repetition threshold for binary rich words is $2+\sqrt{2}/2$. We exhibit the lexicographically least infinite binary rich word attaining this threshold.
DOI : 10.37236/12464
Classification : 68R15
Mots-clés : rich word, repetition threshold, lexicographic order

James D. Currie    ; Narad Rampersad  1

1 Department of Mathematics and Statistics, University of Winnipeg 
@article{10_37236_12464,
     author = {James D. Currie and Narad Rampersad},
     title = {The lexicographically least binary rich word achieving the repetition threshold},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12464},
     zbl = {1560.68141},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12464/}
}
TY  - JOUR
AU  - James D. Currie
AU  - Narad Rampersad
TI  - The lexicographically least binary rich word achieving the repetition threshold
JO  - The electronic journal of combinatorics
PY  - 2024
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.37236/12464/
DO  - 10.37236/12464
ID  - 10_37236_12464
ER  - 
%0 Journal Article
%A James D. Currie
%A Narad Rampersad
%T The lexicographically least binary rich word achieving the repetition threshold
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12464/
%R 10.37236/12464
%F 10_37236_12464
James D. Currie; Narad Rampersad. The lexicographically least binary rich word achieving the repetition threshold. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12464

Cité par Sources :