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Extended triple systems

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

Publisher: Springer
Year: 1972
Tongue: English
Weight: 371 KB
Volume: 8
Category: Article
ISSN: 0001-9054
DOI: 10.1007/bf01844505

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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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It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on v v v points, in such a way that all automorphisms of U can be extended to V, for every admissible v v v satisfying v v v > gðuÞ. We f

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