By Anne E. Edlin and Doron Zeilberger

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Appeared in Advances in Applied Mathematics v. 25 (2000), 228-232.

Written: Feb. 22, 2000.

A method, no matter how powerful and useful, is useless if no one knows about it. Hence John Noonan and Doron Zeilberger did a great service to combinatorial humanity by writing a lucid and clear exposition of the sleeping beauty called the "Goulden-Jackson Cluster Method", extending it at the same time, and finding interesting and novel applications. But there still remained a lot to be done.

In the present article, Edlin and Zeilberger analogize the Goulden-Jackson method to cyclic words, i.e. counting necklaces (with clasps), that do not permit certain patterns as consecutive beads.

IMPORTANT: This article is accompanied by the Maple package CGJ. In fact, the package has it all, and it is more accurate to say that the present article accompanies the package, and is a watered-down version for the benefit of feeble-minded, Maple-illiterate humanoids.

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