\(101\) Anti-Pasch Steiner Triple Systems of Order \(19\)

T. S. Griggs1, J. P. Murphy1
1Department of Mathematics and Statistics Lancashire Polytechnic Preston PRI 2TQ England

Abstract

An algorithm to construct anti-Pasch Steiner triple systems is described and utilized to construct \(101\) such systems of order \(19\). It is also proved that no anti-Pasch \(STS(19)\) contains a non-trivial subsystem. Furthermore, anti-Pasch \(STS(19)\)s with prescribed automorphisms are identified.