Two remarks on Steiner systems

✍ Scribed by Peter J. Cameron

• Publisher: Springer
• Year: 1975
• Tongue: English
• Weight: 847 KB
• Volume: 4
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00148772

✦ Synopsis

In the first part of this paper, those Steiner systems S (3, k, v) are studied in which the set of blocks, or the set of point-pairs, provided with the 'natural' relations, forms an association scheme. Inequalities connecting v and k are derived. These are used to obtain 'geometric' characterisations of certain systems. In the second part, I consider Steiner systems S(t, k, v), with k even and k<2t, in which the symmetric difference of two blocks is a block whenever it has cardinality k. Those with k=2t-2 have already been determined. Here I look briefly at the cases k = 2t-4 and k = t + 1, and show that (t,k)=(5, 6) implies v= 12. This completes the determination of such systems with t~<6 or with k~<8.

STEINER SYSTEMS AND ASSOCIATION SCHEMES