Improved upper and lower bounds on the number of square-free ternary words
are obtained. The upper bound is based on the enumeration of square-free
ternary words up to length 110. The lower bound is derived by constructing
generalised Brinkhuis triples. The problem of finding such triples can
essentially be reduced to a combinatorial problem, which can efficiently be
treated by computer. In particular, it is shown that the number of square-free
ternary words of length n grows at least as 65^(n/40), replacing the previous
best lower bound of 2^(n/17).Comment: 17 pages, AMS LaTeX. Paper has been completely rewritten and
comprises new results on both lower and upper bounds. The Mathematica program
mentioned in the article can be downloaded at
http://mcs.open.ac.uk/ugg2/wordcomb/brinkhuistriples.
