On combinatorial designs

Date of Publication

2009

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

Thesis Adviser

Arlene A. Pascasio

Defense Panel Chair

Jose Tristan F. Reyes

Defense Panel Member

Rigor B. Ponsones
Sonia Y. Tan

Abstract/Summary

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.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU15115

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

iv, 99, [33] leaves, 28 cm.

Keywords

Combinatorial designs and configurations; Combinatorial analysis

Embargo Period

3-30-2021

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