Some operations preserving primitivity of words

Authors:
Jü/rgen Dassow;Gema M. Martí/n;Francisco J. Vico
Affiliations:
Fakultä/t fü/r Informatik, Otto-von-Guericke-Universitä/t Magdeburg, PSF 4120/ D-39016 Magdeburg, Germany;Departamento de Lenguajes y Ciencias de la Computació/n, Universidad de Má/laga, Severo Ochoa, 4, Parque Tecnoló/gico de Andalucí/a, E-29590 Campanillas - Má/laga, Spain;Departamento de Lenguajes y Ciencias de la Computació/n, Universidad de Má/laga, Severo Ochoa, 4, Parque Tecnoló/gico de Andalucí/a, E-29590 Campanillas - Má/laga, Spain
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We investigate some operations where essentially, from a given word w, the word ww^' is constructed where w^' is a modified copy of w or a modified mirror image of w. We study whether ww^' is a primitive word provided that w is primitive. For instance, we determine all cases with an edit distance of w and w^' at most 2 such that the primitivity of w implies the primitivity of ww^'. The operations are chosen in such a way that in the case of a two-letter alphabet, all primitive words of length @?11 can be obtained from single letters.