Date of Publication

8-2025

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with Specialization in Computer Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

John Vincent S. Morales

Defense Panel Chair

April Lynne Say-awen

Defense Panel Member

Luisette C. Candelaria

Abstract (English)

In geometry, a maximal 2-cap in the affine space 𝐴𝐺(𝑛,2) is a collection of points of largest size such that any quadruple of points is in general position. These form a generalization of the question of maximal caps in 𝐴𝐺(𝑛,3), a long-standing problem in combinatorics with connections to and implications for coding theory and other areas. One method used to analyze the structures of caps in 𝐴𝐺(𝑛,3) is to analyze partitions of the space using them. Thus, analogously, this paper identifies the affine symmetry groups of complete and maximal 2-caps in 𝐴𝐺(𝑛,2) for dimensions 𝑛 ≀ 6 and of partitions using them in dimensions 𝑛 ≀ 4, along with some notable examples in dimensions 𝑛 = 5,6, using NumPy and the Qap Visualizer software. This grants deeper insights into the internal and external geometric structure of these 2-caps, which may have implications for their sizes and those of their generalizations.

Abstract Format

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Abstract (Filipino)

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Abstract Format

html

Language

English

Format

Electronic

Keywords

Geometry, Affine; Symmetry groups

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Embargo Period

8-12-2025

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