Geodesic
Complement avoidance in binary words
James Currie1 ; Ľubomíra Dvořáková2 ; Pascal Ochem3 ; Daniela Opočenská4 ; Narad Rampersad1 ; Jeffrey Shallit
1University of Winnipeg
2FNSPE Czech Technical University
3LIRMM
4FNSPE Czech Technical University
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of $\bf w$, then $\overline{x}$ is not a factor of $\bf w$. In particular, we classify such words according to their critical exponents.
DOI : 10.37236/11555
Classification : 68R15

James Currie  1   ; Ľubomíra Dvořáková  2   ; Pascal Ochem  3   ; Daniela Opočenská  4   ; Narad Rampersad  1   ; Jeffrey Shallit 

1 University of Winnipeg
2 FNSPE Czech Technical University
3 LIRMM
4 FNSPE Czech Technical University 
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     author = {James Currie and \v{L}ubom{\'\i}ra Dvo\v{r}\'akov\'a and Pascal Ochem and Daniela Opo\v{c}ensk\'a and Narad Rampersad and Jeffrey Shallit},
     title = {Complement avoidance in binary words},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {4},
     doi = {10.37236/11555},
     zbl = {8120110},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11555/}
}
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James Currie; Ľubomíra Dvořáková; Pascal Ochem; Daniela Opočenská; Narad Rampersad; Jeffrey Shallit. Complement avoidance in binary words. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/11555

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