Extended cyclic triple systems

✍ Scribed by Frank E. Benneit

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 471 KB
• Volume: 24
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90192-9

✦ Synopsis

A:" ex:¢~dod cyclic Wple syste~ is a p;:ir (S. I') where S is a finite set and *3" is a collection of cyclic Mples from S, where eac~ trifle may hwe repeated elements, such ~hat every ordered pair of e emen/s of & not necessarily distinct, is conlai'~ed in exactly one triple ol W. The triples m W arc of three t>,' p.e~< II) {a, a. a}, (2) {b, b, c}, (3) {x, v, z}. where {b. b, c} contains ~.he pai~s b~', bc a~:d cb. whi!e {x, y, z} contains xy, yz and zx but not x:. ',:x or zy. The element :~ is called an idem;)oteat and b a non-idempotent of (& W). We denote by CTS (~;; <~) ghe ciass of all exlende~" cyclic triple ,ystems on ~ elemc.n~s which have ce idempotm~ts. We s~y CFS (n; a) exis*,s if there is a system with paramete,'s n and c~.

We ieve,stigate conditious for the exist(nee of ("FS(n:{~) and show that if the necessaD condition,s are satisfied *.hen CFS (~; c~ e>isvs.