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arXiv · 1508.02793

A generalized Goulden-Jackson cluster method and lattice path enumeration

Yan Zhuang
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Abstract

The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which generalize the combinatorial framework of free monoids. As a sample application of the generalized cluster method, we compute bivariate and multivariate generating functions counting Motzkin paths---both with height bounded and unbounded---by statistics corresponding to the number of occurrences of various subwords, yielding both closed-form and continued fraction formulae.

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Yan Zhuang. 2015-08-12. A generalized Goulden-Jackson cluster method and lattice path enumeration. https://arxiv.org/abs/1508.02793

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