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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).
|Item Type:||Journal Article|
|Extra Information:||The Journal of Integer Sequences is an open access journal without consecutive page numbers. The article number is 01.2.7.
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Uwe Grimm|
|Date Deposited:||13 Feb 2007|
|Last Modified:||24 Feb 2016 10:42|
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