A generalized Goulden–Jackson cluster method and lattice path enumeration
نویسندگان
چکیده
منابع مشابه
A generalized Goulden-Jackson cluster method and lattice path enumeration
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 gen...
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Given a nite or countably in nite set A, let A∗ be the set of all nite sequences of elements of A, including the empty sequence. We call A an alphabet, the elements of A letters, and the elements of A∗ words. By de ning an associative binary operation on two words by concatenating them, we see that A∗ is a monoid under the operation of concatenation, and we call A∗ the free monoid on A. The com...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.09.004