Improved bounds on the number of ternary square-free words
Abstract
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).
Keywords
Cite
@article{arxiv.math/0105245,
title = {Improved bounds on the number of ternary square-free words},
author = {Uwe Grimm},
journal= {arXiv preprint arXiv:math/0105245},
year = {2007}
}
Comments
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.m