A generalized Goulden-Jackson cluster method and lattice path enumeration
Combinatorics
2018-02-20 v3 Discrete Mathematics
Formal Languages and Automata Theory
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.
Cite
@article{arxiv.1508.02793,
title = {A generalized Goulden-Jackson cluster method and lattice path enumeration},
author = {Yan Zhuang},
journal= {arXiv preprint arXiv:1508.02793},
year = {2018}
}
Comments
31 pages