The Fine Intersection Problem for Steiner Triple Systems
โ Scribed by Yeow Meng Chee; Alan C. H. Ling; Hao Shen
- Publisher
- Springer Japan
- Year
- 2008
- Tongue
- English
- Weight
- 127 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract In this paper, we present a conjecture that is a common generalization of the DoyenโWilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ โก 1,3 (mod 6), __u__ < __v__ < 2__u__โ+โ 1, we ask for the minimum __r__ such that there exists a
The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z 0) and intersecting (z 1) cases. When w ! u and v 2w u ร 2z, the elementary necessary conditions are shown to be sufยฎcient for all values o
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 .