Generalized Triad Design Algorithms

This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this s...

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Main Author:	Saa, Tareq Mohammad Abu
Format:	Thesis
Language:	eng
Published:	2012
Subjects:	QA Mathematics
Online Access:	https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf
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id	my-uum-etd.2976
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng
advisor	Ibrahim, Haslinda
topic	QA Mathematics
spellingShingle	QA Mathematics Saa, Tareq Mohammad Abu Generalized Triad Design Algorithms
description	This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this study, generalized and new algorithms for developing TD(v) for any v = 6n + 1 or v = 6n + 5 were developed. In general, the first part of the thesis develops two new techniques to solve the problems above. In addition, new constructions for the starter of a compatible factorization on v objects, a SCF(v), and new algorithms for a CF(v) was developed. The second part of the thesis develops three new techniques for building algorithms of the TD(v), TD(v) = CF(v) where is the completion of the CF(v). Furthermore, a starter triad design, STD(v) = SCF(v) and many remarkable theorems were proved. Additionally, a new technique for STD(v) algorithms, known as the “Generalized Interval Method - GIM” was constructed, by analyzing the pattern of the triples in the STD(v) using the intervals number and the components of triples. This technique, finally listed TD(6n + 1) and TD(6n + 5) by repeated addition of 1 (mod v) from the STD(v).
format	Thesis
qualification_name	Ph.D.
qualification_level	Doctorate
author	Saa, Tareq Mohammad Abu
author_facet	Saa, Tareq Mohammad Abu
author_sort	Saa, Tareq Mohammad Abu
title	Generalized Triad Design Algorithms
title_short	Generalized Triad Design Algorithms
title_full	Generalized Triad Design Algorithms
title_fullStr	Generalized Triad Design Algorithms
title_full_unstemmed	Generalized Triad Design Algorithms
title_sort	generalized triad design algorithms
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2012
url	https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf
_version_	1747827475276103680
spelling	my-uum-etd.29762016-04-27T07:31:52Z Generalized Triad Design Algorithms 2012 Saa, Tareq Mohammad Abu Ibrahim, Haslinda Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA Mathematics This thesis mainly focuses on the development of a triad design on v objects, TD(v), which is a way of arranging distinct triples on v objects with some properties. Previous studies on TD(v) reported its existence when v≡1 or 5 (mod 6) and TD(7) was developed by using a brute-force method. In this study, generalized and new algorithms for developing TD(v) for any v = 6n + 1 or v = 6n + 5 were developed. In general, the first part of the thesis develops two new techniques to solve the problems above. In addition, new constructions for the starter of a compatible factorization on v objects, a SCF(v), and new algorithms for a CF(v) was developed. The second part of the thesis develops three new techniques for building algorithms of the TD(v), TD(v) = CF(v) where is the completion of the CF(v). Furthermore, a starter triad design, STD(v) = SCF(v) and many remarkable theorems were proved. Additionally, a new technique for STD(v) algorithms, known as the “Generalized Interval Method - GIM” was constructed, by analyzing the pattern of the triples in the STD(v) using the intervals number and the components of triples. This technique, finally listed TD(6n + 1) and TD(6n + 5) by repeated addition of 1 (mod v) from the STD(v). 2012 Thesis https://etd.uum.edu.my/2976/ https://etd.uum.edu.my/2976/1/Tareq_Mohammad_Abu_Saa.pdf application/pdf eng validuser Ph.D. doctoral Universiti Utara Malaysia Anderson, I. (1990). Combinatorial designs: Construction method. New York: Ellis Horwood. Anderson, I. (1997). Combinatorial designs and tournaments. USA: Oxford University Press. Böröczky, K. (2004). 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Generalized Triad Design Algorithms

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