Geodesic
Overlap-free symmetric D0L words
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2.

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A D0L word on an alphabet Σ =\0,1,\ldots,q-1\ is called symmetric if it is a fixed point w=\varphi(w) of a morphism \varphi:Σ ^* → Σ ^* defined by \varphi(i)=øverlinet_1 + i øverlinet_2 + i\ldots øverlinet_m + i for some word t_1t_2\ldots t_m (equal to \varphi(0)) and every i ∈ Σ ; here øverlinea means a \bmod q. We prove a result conjectured by J. Shallit: if all the symbols in \varphi(0) are distinct (i.e., if t_i ≠q t_j for i ≠q j), then the symmetric D0L word w is overlap-free, i.e., contains no factor of the form axaxa for any x ∈ Σ ^* and a ∈ Σ . 
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     author = {Frid, Anna},
     title = {Overlap-free symmetric {D0L} words},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2000-2001},
     doi = {10.46298/dmtcs.293},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.293/}
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Frid, Anna. Overlap-free symmetric D0L words. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2. doi : 10.46298/dmtcs.293. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.293/

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