The Goulden-Jackson Cluster Method: Extensions, Applications and Implementations
John Noonan, Doron Zeilberger
Abstract
The powerful (and so far under-utilized) Goulden-Jackson Cluster method for finding the generating function for the number of words avoiding, as factors, the members of a prescribed set of `dirty words', is tutorialized and extended in various directions. The authors' Maple implementations, contained in several Maple packages available from this paper's website (http://www.math.temple.edu/~zeilberg/gj.html), are described and explained.
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