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A Mass Formula for Steiner Triple Systems STS(2n−1) of 2-Rank 2n−n

✍ Scribed by Vladimir D. Tonchev

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
116 KB
Volume
95
Category
Article
ISSN
0097-3165

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✦ Synopsis

A formula is found for the total number of distinct Steiner triple systems on 2 n &1 points whose 2-rank is one higher than the possible minimum 2 n &n&1. The formula can be used for deriving bounds on the number of pairwise nonisomorphic systems for large n, and for the classification of all nonisomorphic systems of small orders. It is proved that the number of nonisomorphic Steiner triple systems on 2 n &1 points of 2-rank 2 n &n grows exponentially.

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