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Transitive Steiner triple systems of order 25

✍ Scribed by Vladimar D Tonchev


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
211 KB
Volume
67
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


The 2-rotational Steiner triple systems
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In this paper, we enumerate the 2-rotational Steiner triple systems of order 25. There are exactly 140 pairwise non-isomorphic such designs. All these designs have full automorphism groups of order 12. We also investigate the existence of subsystems and quadrilaterals in these designs.

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## 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

A construction of cyclic Steiner triple
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## Phelps 2.1 will produce such a collection for each n -1/> 1. Choose U as in (3.1) above, then B,, =pBn-1 U U is a set of representatives for a CSTS(p"). Since every multiplier m =-1 (modp n'l) is an automorphism of this system f(x)=p"-lx2 +x will be an isomorphism from B,, to another CSTS(p~),

Another complete invariant for Steiner t
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## 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