Abstract
A Steiner quadruple system of order n is said to be cyclic if it has an n-cycle as an automorphism. In this paper we enumerate all cyclic Steiner quadruple systems of order 20. As a necessary prelude to this enumeration, a number of results are established, including a new characterization of the existence problem in terms of hypergraphs. It is also shown that the necessary conditions for an S-cyclic SQS (n) is that n=2, 4, 10 or 20 mod 24, and that there does exist an infinite class of cyclic Steiner quadruple systems, thus answering a question posed by Lindner and Rosa [16].
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