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Improved bounds on the number of ternary square-free words

By Uwe Grimm

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)

Year: 2001
OAI identifier: oai:oro.open.ac.uk:6744
Provided by: Open Research Online

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