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Mathematical Properties and Interactions of Catalan Numbers and Symmetry Groups
- 1 Rosedale Global High School, Markham, L3R 6G2, Canada
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Abstract
This study focuses on the history of Catalan numbers, including definitions, formulas, combinatorial meanings, and geometric interpretations. Catalan numbers are a sequence of natural numbers widely used in combinatorial mathematics, often used to represent arrangements of structures such as balanced brackets, binary trees and polygonal triangular dissections. In terms of the definition and properties of symmetry groups, the study includes the structure of orders and subgroups as well as representation theory. Symmetry groups describe the symmetry of geometric objects, including rotations, reflections, and axes of rotational reflections. The connection between Catalan numbers and symmetry groups, including influences and interactions, is further analysed.
Keywords
Catalan numbers, Symmetric groups, Mathematical characteristics, Connection
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Cite this article
Li,X. (2025). Mathematical Properties and Interactions of Catalan Numbers and Symmetry Groups. Theoretical and Natural Science,108,78-87.
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Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
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