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A special class of nested Steiner triple systems

✍ Scribed by Darryn E. Bryant

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 219 KB
Volume: 152
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00247-g

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✦ Synopsis

There exists a pair of (v, 4, 1)-BIBD's, with block sets B 1 and B 2 , such that it is possible to obtain a Steiner triple system by removing a point from each block in B 1 U B 2 if and only if v == 1 (mod 12). A Steiner triple system of order v (denoted STS(v)) is a (v, 3, 1)-BlBD. A nested Steiner triple system of order v (denoted NSTS(v)) is an STS(v) with an extra point added to each block in such a way that the resulting blocks form a (v, 4, 2)-BlBD. After several earlier papers on NSTS's (see e.g. [2,3] Stinson [4] constructed NSTS(v)'s for each v == 1 (mod 6). It is easy to see that v == 1 (mod 6) is necessary.

In this paper, we consider a special class of NSTS(v)'s; those in which the (v, 4, 2)-BlBD can be partitioned into two (v, 4, 1)-BlBD's. These will be called partitionable nested Steiner triple systems.

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