Steiner triple systems with transrotational automorphisms
β Scribed by Robert B. Gardner
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 373 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A Steiner triple system of order u is said to be k-transrotational if it admits an automorphism consisting of a fixed point, a transposition, and k cycles of length (u-3)/k. Necessary and sufficient conditions are given for the existence of l-and 2-transrotational Steiner triple systems.
π SIMILAR VOLUMES
It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on v v v points, in such a way that all automorphisms of U can be extended to V, for every admissible v v v satisfying v v v > gΓ°uΓ. We f
To pattittrm, tnto oil ttme 2 Srciner ## 1. lntroductian 1 refer to 131 for the history of the problem. which goes back to 1850; in fxt, Caylcy [ I] showed that there is no packing of arder 7. The existence of a packi!ng of order 9 was discovered by Kirkman 141, and rectiscsvcred ?~erdI t imcs; bu
and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press ## 1. Introduction A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that eve