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The existence of reverse Steiner triple systems

✍ Scribed by Luc Teirlinck

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
184 KB
Volume
6
Category
Article
ISSN
0012-365X

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✦ Synopsis

A Steiner triple system of order u is called reverse if its automorphism group contains an involution fixing only one point. We show mat such a system exists if and only if u = 1,3, 9 or 19 (mod 24).

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On reverse Steiner triple systems
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✍ Alexander Rosa πŸ“‚ Article πŸ“… 1972 πŸ› Elsevier Science 🌐 English βš– 950 KB

1 he existence of reverse Steiner triple systems It.e. Steiner triple systems with a given involutory automorphism of speck4 type) is investigated. it is srfrwrn that such a system exists far alI wders n if n z t of 3 or 9 (mod 24: except posd&ly far n = 25. A system with this grspetty exists also f

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## Abstract We consider two well‐known constructions for Steiner triple systems. The first construction is recursive and uses an STS(__v__) to produce a non‐resolvable STS(2__v__ + 1), for __v__ ≑ 1 (mod 6). The other construction is the Wilson construction that we specify to give a non‐resolvable

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If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i