Square-free partial words

Authors:
Vesa Halava;Tero Harju;Tomi Kärki
Affiliations:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland
Venue:
Information Processing Letters
Year:
2008

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Abstract

We say that a partial word w over an alphabet A is square-free if every factor xx^' of w such that x and x^' are compatible is either of the form @?a or a@? where @? is a hole and a@?A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes.