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A class of Steiner triple systems of order $21$ and associated Kirkman systems

Authors: Rudolf A. Mathon, Kevin T. Phelps and Alexander Rosa
Journal: Math. Comp. 37 (1981), 209-222
MSC: Primary 05B07; Secondary 51E10
Addendum: Math. Comp. 64 (1995), 1355-1356.
MathSciNet review: 616374
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Abstract: We examine a class of Steiner triple systems or order 21 with an automorphism consisting of three disjoint cycles of length 7. We exhibit explicitly all members of this class: they number 95 including the 7 cyclic systems. We then examine resolvability of the obtained systems; only 6 of the 95 are resolvable yielding a total of 30 nonisomorphic Kirkman triple systems of order 21. We also list several invariants of the systems and investigate their further properties.

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Keywords: Steiner triple system, Kirkman triple system, isomorphism, resolvability
Article copyright: © Copyright 1981 American Mathematical Society