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Cyclic and rotational hybrid triple systems

✍ Scribed by Robert Gardner; Biagio Micale; Mario Pennisi; Rebecca Zijlstra

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 669 KB
Volume: 171
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00036-2

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Cyclic and rotational hybrid triple syst

Cyclic and rotational hybrid triple systems

✍ Robert Gardner; Biagio Micale; Mario Pennisi; Rebecca Zijlstra 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 664 KB

A hybrid triple system of order v, denoted HTS(v), is said to be cyclic if it admits an automorphism consisting of a single cycle of length v. A HTS(v) admitting an automorphism consisting of a fixed point and a cycle of length v -1 is said to be rotational. Necessary and sufficient conditions are g

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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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We develop some recursive constructions for rotational Steiner triple systems with which the spectrum of a k-rotational Steiner triple system of order v is completely determined for each positive integer k .

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A transitive triple, (a,b,c), is defined to be the set )} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D, p), where D is a set of v points and fi is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is