On regular and 2-scored 2-orthogonal tournaments

• Main Author: Urbano, Reynaldo M.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Orthogonal polynomials; Mathematics > Formulae; Graph theory; Analytic functions; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1564; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8402/viewcontent/TG02251_F_Redacted.pdf
• Institution: De La Salle University

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.