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Completing the spectrum of rotational Mendelsohn triple systems

โœ Scribed by Zhike Jiang; Charles J. Colbourn


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
356 KB
Volume
183
Category
Article
ISSN
0012-365X

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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 cyclic triple (a, b, c) is defined to be set { (a, b) ,(b,c),(c,a)} of ordered pairs. A Mendelsohn triple system of order v, M(2,3, u), is a pair (M, fi), w h ere M is a set of u points and fi is a collection of cyclic triples of pairwise distinct points of M such that any ordered pair of distinct

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โœ F. E. Bennett; R. Wei ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 792 KB

In this article it is shown that any resolvable Mendelsohn triple system of order u can be embedded in a resolvable Mendelsohn triple system of order v iff v 2 3u, except possibly for 71 values of (u,v). 0 1993 John Wiley & Sons, Inc. ## Theorem 1.1. A RMTS(v) exists if and only if If ( X , % ) a

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The spectrum for LMTS(v, 1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS(v,3). Furthermore, by the existence of LMTS(v, 1) and LMTS(v, 3), the spectrum for LMTS(v, A) is completed, that is Y = 2 (mod A), v 2 A + 2, if A # 0 (m

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## Abstract It is proved in this article that the necessary and sufficient conditions for the embedding of a ฮปโ€fold pure Mendelsohn triple system of order __v__ in ฮปโ€__fold__ pure Mendelsohn triple of order __u__ are ฮป__u__(__u__ โˆ’ 1) โ‰ก 0 (mod 3) and __u__ โฉพ 2__v__ + 1. Similar results for the embe