Project/Area Number  01540086 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
代数学・幾何学

Research Institution  Meijo University 
Principal Investigator 
ITO Noboru Meijo University, Department of Mathematics, Professor, 理工学部, 教授 (20151524)

CoInvestigator(Kenkyūbuntansha) 
北條 俊一 甲南大学, 理学部, 教授 (00084856)
TAGUTI Tomoyasu Kokan University, Department of Applied Mathematics, Professor, 理学部, 教授 (30140388)
FURUYA Mamoru Meijo University, Department of Mathematics, Professor, 理工学部, 教授 (80076520)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1990 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1989 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Hadamard Tournament / Even Tournament / Regular Tournament / Cyclic Tournament / Hamming Weight / Nearly Triple Regular / 3Blocks Intersection Number / アダマルトナメント / 偶トナメント / 巡回トナメント / ハミング重み / 近3重対称デザイン / 3ーブロック交差数 / 正則トナメント / 巡回符号 / 対称群 / 直交トナメント / 反直交トナメント / 近3正則対称デザイン / 2重正則単向グラフ 
Research Abstract 
(1) We have shown that there exists a regular even tournament for every positive integer v such that v is congruentto 3 modulo 8. (2) We have solved the existence problem for cyclic even tournaments. If v is congruent to 3 modulo 8, then a cyclic even tournament of order v exists if and only if 2 has a singly even order for every prime factor p of v. If v is congruent to 1 modulo 8, then a cyclic even tournament of order v exists if and only if 2 has an odd order for every prime factor p of v. In the second case an intimate relation with a binary cyclic code where the Hamming weight of every code word is a multiple of 4 exists. (3) We have determined the largest number which may be the order of the automorphism group G of a cyclic tournament of order v and the structure of G in such a case. (4) We have improved results of Alspach and Berggren concerning a tournament of order v whose automorphism group has the largest order. Namely we obtained necessary and sufficient conditions for v such that the group is a 3group or (3, 5)group. (5) We together with Raposa in Manila, Philippines have shown that the 3intersection number pair is unique for a nearly triply regular symmetric design of RHtype.
