Refereed article in compilation book (A3)
Minimal Similarity Relations for Square-Free Words
List of Authors: T. Harju, T. Kärki
Editors: Gh. Paun, G. Rozenberg, A. Salomaa
Place: Bucharest
Publication year: 2014
Book title *: Discrete Mathematics and Computer Science. In Memoriam Alexandru Mateescu (1952-2005)
Start page: 193
End page: 200
ISBN: 978-973-27-2470-5
A relation R on words is a similarity relation if it is reflexive, symmetric and it is generated by letters. A word w is said to be R-square–free, if it has no factors of the form uv where u and v are related by R. We give a new proof for the result of Kärki [Fund. Inform., 116 (2012)] that the smallest similarity relation that gives an infinite square–free word is generated by six pairs.We also characterize all trees of order six corresponding to the similarity relations that admit a square–free word.