Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

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DMTCS vol 4 no 2 (2001), pp. 357-362

Discrete Mathematics & Theoretical Computer Science


Volume 4 n° 2 (2001), pp. 357-362

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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