## Abstract In this paper, we present three constructions for antiβmitre Steiner triple systems and a construction for 5βsparse ones. The first construction for antiβmitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class mod
The resolution of the anti-mitre Steiner triple system conjecture
β Scribed by Adam Wolfe
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 106 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
Abstract
This paper gives a proof of the existence of antiβmitre Steiner triple systems of order n for every nββ‘β1,3 mod 6 except for nβ=β9. Β© 2005 Wiley Periodicals, Inc. J Combin Designs 14: 229β236, 2006
π SIMILAR VOLUMES
Geometric properties are used to determine the chromatic number of AG(4, 3) and to derive some important facts on the chromatic number of PG(n, 2). It is also shown that a 4-chromatic STS(v) exists for every admissible order v β₯ 21.
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
Formulae for the numbers of two, three, and four-line configurations in a Steiner triple system of order u, STS(u), are given. While the formulae for two and three-line configurations depend only on u , the same is true for only 5 of the 16 four-line configurations. For the other 11 and fixed u, the