On Kirkman triple systems of order 33
โ Scribed by Vladimir D. Tonchev; Scott A. Vanstone
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 259 KB
- Volume
- 106-107
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
from the 84 cyclic STS(33).
๐ SIMILAR VOLUMES
Let J R (v) denote the set of all integers k such that there exists a pair of KTS(v) with precisely k triples in common. In this article we determine the set J R (v) for v#3 (mod 6) (only 10 cases are left undecided for v=15, 21, 27, 33, 39) and establish that J R (v)=I(v) for v#3 (mod 6) and v 45,
## Abstract A __large set__ of Kirkman triple systems of order __v__, denoted by __LKTS__(__v__), is a collection {(__X__, __B~i~__) : 1โโคโ__i__โโคโ__v__โโโ2}, where every (__X__,__B~i~__) is a __KTS__(__v__) and all __B~i~__ form a partition of all triples on __X__. Many researchers have studied th
There are 80 non-isomorphic Steiner triple systems of order 15. A standard listing of these is given in Mathon et al. (1983, Ars Combin., 15, 3-110). We prove that systems #1 and #2 have no bi-embedding together in an orientable surface. This is the first known example of a pair of Steiner triple sy