Discrete Mathematics & Theoretical Computer Science
| author: | Anna Frid |
|---|---|
| title: | Overlap-free symmetric D0L words |
| keywords: | overlap-free word, D0L word, symmetric morphism |
| abstract: | A D0L word on an alphabet Σ={0,1,..,q-1} is called symmetric if it is a fixed point w=Φ(w) of a morphism Φ:Σ* → Σ* defined by Φ(i)=t1 + i t2 + i.. tm + i for some word t1t2..tm (equal to Φ(0)) and every i ∈ Σ; here a means a mod q.
We prove a result conjectured by J. Shallit: if all the symbols in Φ(0) are distinct (i.e., if ti ≠ tj for i ≠ 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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| reference: | Anna Frid (2001), Overlap-free symmetric D0L words, Discrete Mathematics and Theoretical Computer Science 4, pp. 357-362 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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