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A branch of combinatorics that focuses on the study of words and formal languages
2
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What is the cardinality of the set of Dyck natural numbers of semilength $k$?
In arXiv:2102.02777 ("Recursive Prime Factorizations: Dyck Words as Numbers"), I show that there is a 1:1 correspondence between $\mathbb{N} = \{0,1,2,3,4,\ldots\}$ and $\mathcal{D}_{r_{\text{min}}} = …
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Prove using Dyck naturals: for $n \in \mathbb{N}_{+}$ and big enough $k \in \mathbb{N}_{+}$,...
While conducting research in connection with arXiv:2102.02777 ("Recursive Prime Factorizations: Dyck Words as Numbers"), I noticed certain interesting patterns, one of which inspired the following co …