The many names of (7, 3, 1): An exposition

• Main Authors: Guittap, Aldwin, Hervera, Hilda
• Format: text
• Language: English
• Published: Animo Repository 2006
• Subjects: Graph theory; Matrices; Combinatorial designs and configurations; Finite geometries; Hadamard matrices
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17427
• Institution: De La Salle University

This thesis is an exposition of the article The Many Names of (7, 3, 1) by Ezra Brown which appeared in the 2002 issue of the Mathematics Magazine, Volume 75. The thesis discusses the (7, 3, 1) design and how it serves as a common link to three branches of mathetics namely, Graph Theory, Combinatorial Designs, and Finite Geometry. In Graph Theory, a (7, 3, 10 design represents a doubly regular tournament which in turn generates Hadamard matrices. The (7, 3, 1) is a balanced incomplete (7, 7, 3, 3, 1) block design of Combinatorial Design Theory. The (7, 3, 1) design is also The Fano projective plane. Relationships existing between projective planes and complete set of orthogonal Latin squares are discussed in detail and illustrations.