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
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
Recommended Citation
Cabral, K., & Olayvar, A. V. (2009). On combinatorial designs. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/5030
Embargo Period
3-30-2021