Overlap-free symmetric D0L words - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2001

Overlap-free symmetric D0L words


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 .
Fichier principal
Vignette du fichier
dm040220.pdf (51.56 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00958967 , version 1 (13-03-2014)



Anna Frid. Overlap-free symmetric D0L words. Discrete Mathematics and Theoretical Computer Science, 2001, Vol. 4 no. 2 (2), pp.357-362. ⟨10.46298/dmtcs.293⟩. ⟨hal-00958967⟩


40 View
698 Download



Gmail Facebook X LinkedIn More