On regular and 2-scored 2-orthogonal tournaments - Urbano, Reynaldo M. (Animo Repository, 1994)
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.