Cyclic and rotational hybrid triple systems
โ Scribed by Robert Gardner; Biagio Micale; Mario Pennisi; Rebecca Zijlstra
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 664 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
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 given for the existence of a cyclic HTS(v) and a rotational HTS(v).
๐ SIMILAR VOLUMES
A:" ex:ยข~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
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 .
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