Let RB(3, \*; v) denote a resolvable \*-fold triple system of order v. It is proved in this paper that the necessary and sufficient conditions for the embedding of an RB(3, \*; v) in an RB(3, \*; u) are u 3v and (i) u#v#3 (mod 6) if \*#1 (mod 2), (ii) u#v#3 (mod 3) if \*#0 (mod 4), or (iii) u#v#0 (m
Embeddings of almost resolvable triple systems
β Scribed by Zhiqiang Liu; Hao Shen
- Book ID
- 108315786
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 174 KB
- Volume
- 261
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
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
An MTS(v) [or DTS(v)] is said to be resolvable, denoted by RMTS(v) [or RDTS(v)], if its block set can be partitioned into parallel classes. An MTS(v) [or DTS(v)] is said to be almost resolvable, denoted by ARMTS(v) [or ARDTS(v)], if its bloak set can be partitioned into almost parallel classes. The
## Abstract The purpose of this paper is the initiation of an attack on the __general existence problem__ for almost resolvable 2__k__βcycle systems. We give a complete solution for 2__k__=6 as well as a complete solution modulo one possible exception for 2__k__=10 and 14. We also show that the exi
If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i
## Abstract We consider two wellβknown constructions for Steiner triple systems. The first construction is recursive and uses an STS(__v__) to produce a nonβresolvable STS(2__v__β+β1), for __v__ββ‘β1 (mod 6). The other construction is the Wilson construction that we specify to give a nonβresolvable