# 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 defined by ^{*} → Σ^{*}Φ(i)=t for some word _{1} + i t_{2} + i.. t_{m} + it (equal to _{1}t_{2}..t_{m}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 t for _{i} ≠ t_{j}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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