Some results on Dyck paths and Motzkin paths
Stefano Capparelli, Alberto Del Fra
TL;DR
This paper introduces an equivalence relation on Dyck paths, develops formulas for class sizes, and derives combinatorial formulas for counting Dyck and Motzkin paths of fixed length.
Contribution
It presents a new equivalence relation on Dyck paths and provides formulas for class sizes and path enumeration, advancing combinatorial understanding.
Findings
Formulas for the cardinality of equivalence classes
Combinatorial formulas for Dyck path counts
Enumeration of Motzkin paths of fixed length
Abstract
We introduce an equivalence relation on the set of Dyck paths and some operations on them. We determine a formula for the cardinality of those equivalence classes and use this information to obtain a combinatorial formula for the number of Dyck and Motzkin paths of a fixed length.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Topological and Geometric Data Analysis