|Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.7|
Institute of Mathematics
Silesian University of Technology
We study diverse problems concerning extensions of words preserving the property of avoiding squares. Our main motivation is the conjecture stating that there are no extremal words over a 4-letter alphabet. We also investigate a natural recursive procedure of generating squarefree words by a single-letter rightmost extension. We present the results of computer experiments supporting a supposition that this procedure gives an infinite squarefree word over any alphabet of size at least three.
(Concerned with sequence A006742.)
Received May 1 2021; revised versions received May 4 2021; August 17 2021; August 30 2021. Published in Journal of Integer Sequences, September 23 2021.