Generalizations of the Goulden-Jackson Cluster Method

Details Generalizations of the Goulden-Jackson Cluster Method Generalizations of the Goulden-Jackson Cluster Method

2008-10-28

arxiv.org/abs/0810.5113v1

Mathematics

Combinatorics

18 pages

Scientific paper

We give several modifications of the Goulden-Jackson Cluster method for finding generating functions for words avoiding a given set of forbidden words. Our modifications include functions which can take into account various 'weights' on words, including single letter probability distributions, double letter (i.e. pairwise) probability distributions, and triple letter probability distributions. We also describe an alternative, recursive approach to finding such generating functions. We describe Maple implementations of the various modifications. The accompanying Maple package is available at the website for this paper.

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