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Overlap-free symmetric D0L words

Abstract : 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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Submitted on : Thursday, March 13, 2014 - 4:53:52 PM
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Anna Frid. Overlap-free symmetric D0L words. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, Vol. 4 no. 2 (2), pp.357-362. ⟨10.46298/dmtcs.293⟩. ⟨hal-00958967⟩



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