## Abstract In this paper, we present a conjecture that is a common generalization of the DoyenβWilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ β‘ 1,3 (mod 6), __u__ < __v__ < 2__u__β+β 1, we ask for the minimum __r__ such that there exists a
On the Intersection Problem for Steiner Triple Systems of Different Orders
β Scribed by Peter Danziger; Peter Dukes; Terry Griggs; Eric Mendelsohn
- Publisher
- Springer Japan
- Year
- 2006
- Tongue
- English
- Weight
- 200 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper, we enumerate the 2-rotational Steiner triple systems of order 25. There are exactly 140 pairwise non-isomorphic such designs. All these designs have full automorphism groups of order 12. We also investigate the existence of subsystems and quadrilaterals in these designs.
## Abstract In this note, the 80 nonβisomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of t