First Written: May 1, 1997. Last Update: May 13, 1997.

The Goulden-Jackson method was (until the appearance of this paper), one of the most well-kept secrets in combinatorics. In this paper we give away this secret, and generalize it in various directions. Most importantly, we wrote many Maple programs implementing the method and its extensions.

Most importantly, look up the paper's Very own Web Page , that contains lots of very useful Maple packages, that are mentioned in the paper .

One of the applications mentioned in our paper is to the enumeration of square-free ternary words that appeared in his book `Matheamtical Constants'.

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