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Determination of Steiner Triple Systems of Order 15

✍ Scribed by Marshall Hall, Jr. and J. D. Swift

Book ID
121474267
Publisher
American Mathematical Society
Year
1955
Weight
777 KB
Volume
9
Category
Article
ISSN
0891-6837

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πŸ“œ SIMILAR VOLUMES

Steiner triple systems of order 15 and t
Steiner triple systems of order 15 and their codes
✍ Vladimir D. Tonchev; Robert S. Weishaar πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 392 KB

The binary linear codes generated by incidence matrices of the 80 Steiner triple systems on 15 points (STS( )) are studied. The 80 codes of length 35 spanned by incidence vectors of the points are all non-isomorphic. In contrast, a pair of codes of length 15 generated by blocks are isomorphic if and

Another complete invariant for Steiner t
Another complete invariant for Steiner triple systems of order 15
✍ Olivier Anglada; Jean-FranΓ§ois Maurras πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 64 KB

## Abstract In this note, the 80 non‐isomorphic 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

On the Bi-embeddability of Certain Stein
On the Bi-embeddability of Certain Steiner Triple Systems of Order 15
✍ G.K. Bennett; M.J. Grannell; T.S. Griggs πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 57 KB

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

Quasi-embeddings of Steiner triple syste
Quasi-embeddings of Steiner triple systems, or Steiner triple systems of different orders with maximum intersection
✍ Peter Dukes; Eric Mendelsohn πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 182 KB

## Abstract In this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ ≑ 1,3 (mod 6), __u__ < __v__ < 2__u__ +  1, we ask for the minimum __r__ such that there exists a