Geodesic
Extremal overlap-free and extremal \(\beta\)-free binary words
Lucas Mol1 ; Narad Rampersad2 ; Jeffrey Shallit3
1University of Winnipeg
2The University of Winnipeg
3University of Waterloo
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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An overlap-free (or $\beta$-free) word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ at any position contains an overlap (or a factor of exponent at least $\beta$, respectively). We find all lengths which admit an extremal overlap-free binary word. For every "extended" real number $\beta$ such that $2^+\leqslant\beta\leqslant 8/3$, we show that there are arbitrarily long extremal $\beta$-free binary words.
DOI : 10.37236/9703
Classification : 68R15, 68V15
Mots-clés : extremal words, overlap-free words, power-free words

Lucas Mol  1   ; Narad Rampersad  2   ; Jeffrey Shallit  3

1 University of Winnipeg
2 The University of Winnipeg
3 University of Waterloo 
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     author = {Lucas Mol and Narad Rampersad and Jeffrey Shallit},
     title = {Extremal overlap-free and extremal \(\beta\)-free binary words},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9703},
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Lucas Mol; Narad Rampersad; Jeffrey Shallit. Extremal overlap-free and extremal \(\beta\)-free binary words. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9703

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