Date of Publication

9-9-1994

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Blesilda P. Raposa

Defense Panel Chair

Severino Gervacio

Defense Panel Member

Severino Diesto
Yolando Beronque

Abstract/Summary

Let v be a positive integer such that v = 3 (modulo 8). Let A be a tournament of order v, then, A is 2-orthogonal if the product AAt equals I where the multiplication is modulo 2, At is the transpose of A and I is the identity matrix. This study presents two main theorems the first shows the existence of regular 2-orthogonal tournaments of order v while the second shows the existence of 2-scored 2-orthogonal tournaments. Aside from these two theorems, this paper also includes other theorems necessary in the study of 2-orthogonal tournaments relative to its score set. It presents all the proofs to the theorems and propositions as given in Noboru Ito's paper entitled On 2-Orthogonal Tournaments which appears in the Proceedings 22nd Annual Meeting, Iranian Mathematical Society.Let v be a positive integer such that v = 3 mod 8. Let A be a tournament of order v then A is 2-orthogonal if the product AAT equals I where the multiplication is modulo 2, AT is the transpose of A and I is the identity matrix. This study presents two main theorems: the first shows the existence of regular 2-orthogonal tournaments of order v while the second shows the existence of 2-scored 2-orthogonal tournaments. Likewise, this paper includes other theorems necessary in the study of 2-orthogonal tournaments relative to the score set. It presents all the proofs to the theorems and propositions as given in Noboru Ito's paper entitled On 2-Orthogonal Tournaments which will appear in the Proceedings 22nd Annual Meeting, Iranian Mathematical Society.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG02251

Shelf Location

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

Physical Description

98 leaves

Keywords

Orthogonal polynomials; Mathematics--Formulae; Graph theory; Analytic functions

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