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Journal of Discrete Mathematical Sciences and Cryptography cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Combinatorial applications of the Catalan numbers in structuring discrete mathematical models

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pp. 299–306Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2486 Crossmark XML
Received:
09 Apr 2025
Published Online:
31 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2486
Pages:
299–306

Abstract

Many discrete mathematics models emphasize the Catalan numbers, a series of natural integers important in combinatory. These numbers also appear in lattice routes, binary bushes, and create triangulations. This study uses combinatorial methods to organize discrete arithmetic models using Catalan numbers. It emphasizes algebraic combinatory, geometry, and plan idea. We show how Catalan numbers regulate combinatorial devices and use them to create form analysis algorithms and solve optimization problems. We demonstrate how they may be used to count optimal search tree topologies, non-crossing partitions, and planar graphs. We also provide unique approaches to extend Catalan-based models to higher dimensions, increasing their relevance in modern mathematical modelling.

Keywords

Subject Classifications

68R05

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