Generating function for Naturalized Series: The case of Ordered Motzkin Words
Gennady Eremin

TL;DR
This paper derives a generating function for a restricted class of Motzkin words, which are balanced parentheses with zeros, under specific constraints like no leading zeros, expanding combinatorial enumeration methods.
Contribution
It introduces a new generating function for modified Motzkin words with restrictions, advancing the analytical tools for combinatorial object enumeration.
Findings
Derived the generating function for restricted Motzkin words
Analyzed the combinatorial properties of zero-restricted Motzkin words
Extended the application of generating functions to new combinatorial constraints
Abstract
We continue to consider the ordered lexicographic sequence, which is constructed according to the formal characteristics of a series of natural numbers. For analysis, we selected balanced parentheses with zeros, Motzkin words. As you know, generating functions allow you to work with combinatorial objects by analytical methods. Motzkin words are enumerated by Motzkin numbers, for the generation of which there is a corresponding generating function. In our case, restrictions are imposed on Motzkin words, for example, there are no leading zeros in bracket sets. The purpose of this article is to obtain the generating function of such modified Motzkin words.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · semigroups and automata theory
