A Study in Steiner Quadruple Systems

Abstract

<p> This thesis is a contribution to the theory of Steiner quadruple systems. The first chapter provides a construction of resolvable Steiner quadruple systems that is different from the known constructions. In the second chapter, we construct Steiner quadruple systems with an automorphism that consists of a cycle of length 2 plus a cycle of full length minus 2, and investigate the number of pairwise distinct systems of this kind. In the third chapter, we also construct non-S-cyclic Steiner quadruple systems, one of which is an answer to a question raised in [11], and also investigate the number of pairwise distinct systems.</p>