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Extended triple systems

✍ Scribed by D. M. Johnson; N. S. Mendelsohn

Publisher: Springer
Year: 1971
Tongue: English
Weight: 53 KB
Volume: 7
Category: Article
ISSN: 0001-9054
DOI: 10.1007/bf01818531

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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 a

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In this paper, we show that any partial extended triple system (partial totally symmetric quasigroup) of order n can be embedded in a totally symmetric quasigroup of order v, v >~4n +6, v -= 2(mod4). This bound can be lowered to 4n + 2 in most cases.

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