On combinatorial designs

• Main Authors: Cabral, Kylie Ivet, Olayvar, Angelica V.
• Format: text
• Language: English
• Published: Animo Repository 2009
• Subjects: Combinatorial designs and configurations; Combinatorial analysis; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/5030
• Institution: De La Salle University

This thesis is an exposition of some sections of the tenth chapter of the book entitled Introductory Combinatorics by Richard A. Brualdi, published in 1999 by Prentice-Hall Inc. It discusses the concepts and examples of balanced incomplete block designs, symmetric balanced incomplete block designs, Steiner triple systems, resolvable block designs, Kirkman systems, Latin squares and mutually orthogonal Latin squares. Relationships existing between parameters of a balanced incomplete block designs were discussed. It also presents the construction of resolvable balanced incomplete block designs and mutually orthogonal Latin squares. The conditions for the existence of mutually orthogonal Latin squares are discussed in detail. This thesis focuses on the following main theorem: for every integer n > 2, there exists n - 1 mutually orthogonal Latin squares of order n if and only if there exists a resolvable balanced incomplete block design with n2 varieties, n2 + n blocks each of size n, and with index and replication number equal to 1 and n + 1, respectively. For clarity of discussion, the researchers provide explicit constructions of Latin squares and balanced incomplete designs.