Frame Self-orthogonal Mendelsohn Triple Systems
โ Scribed by Yun Qing Xu*; Han Tao Zhang**
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2004
- Tongue
- English
- Weight
- 187 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Two Steiner triple systems, S 1 VY B 1 and S 2 VY B 2 , are orthogonal (S 1 c S 2 ) if B 1 B 2 Y and if fuY vg T fxY yg, uvwY xyw P B 1 , uvsY xyt P B 2 then s T t. The solution to the existence problem for orthogonal Steiner triple systems, (OSTS) was a major accomplishment in design theory. Two or
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
## Bennett, F.E. and H. Shen, On indecomposable pure Mendelsohn triple systems, Discrete Mathematics 97 (1991) 47-57. Let u and I be positive integers. A Mendelsohn triple system MTS(u, A) is a pair (X, a), where X is a u-set (of points) and %? is a collection of cyclically ordered 3-subsets of X
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