| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 8903111 | Discrete Mathematics | 2018 | 22 Pages |
Abstract
The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions 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 formulas.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yan Zhuang,